Precalculus
11th Edition
ISBN: 9780135189405
Author: Michael Sullivan
Publisher: PEARSON
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Chapter 3.4, Problem 37AYU
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Chapter 3 Solutions
Precalculus
Ch. 3.1 - Graph.
Ch. 3.1 - Find the slope of the line joining the points (...Ch. 3.1 - Find the average rate of change of from to
Ch. 3.1 - Solve: 6x900=15x+2850 . (pp. A44-A46)Ch. 3.1 - If f( x )= x 2 4 , find f( 2 ) . (pp. 60-62)Ch. 3.1 - True or False The function is increasing on the...Ch. 3.1 - For the graph of the linear function f( x )=mx+b ,...Ch. 3.1 - If the slope m of the graph of a linear function...Ch. 3.1 - True or False The slope of a nonvertical line is...Ch. 3.1 - True or False The average rate of change of f( x...
Ch. 3.1 - What is the only type of function that has a...Ch. 3.1 - A car has 12,500 miles on its odometer. Say the...Ch. 3.1 - In Problems 13-20, a linear function is given. a....Ch. 3.1 - In Problems 13-20, a linear function is given. a....Ch. 3.1 - In Problems 13-20, a linear function is given. a....Ch. 3.1 - In Problems 13-20, a linear function is given. a....Ch. 3.1 - In Problems 13-20, a linear function is given. a....Ch. 3.1 - In Problems 13-20, a linear function is given. a....Ch. 3.1 - In Problems 13-20, a linear function is given. a....Ch. 3.1 - In Problems 13-20, a linear function is given. a....Ch. 3.1 - In Problems 21-28, determine whether the given...Ch. 3.1 - In Problems 21-28, determine whether the given...Ch. 3.1 - In Problems 21-28, determine whether the given...Ch. 3.1 - In Problems 21-28, determine whether the given...Ch. 3.1 - In Problems 21-28, determine whether the given...Ch. 3.1 - In Problems 21-28, determine whether the given...Ch. 3.1 - In Problems 21-28, determine whether the given...Ch. 3.1 - In Problems 21-28, determine whether the given...Ch. 3.1 - Suppose that f( x )=4x1 and g(x)=2x+5 . a. Solve...Ch. 3.1 - Suppose that f( x )=3x+5 and g(x)=2x+15 . a. Solve...Ch. 3.1 - In parts (a) - (f), use the following figure. a....Ch. 3.1 - In parts (a) - (f), use the following figure. a....Ch. 3.1 - In parts (a) and (b), use the following figure. a....Ch. 3.1 - In parts (a) and (b), use the following figure. a....Ch. 3.1 - In parts (a) and (b), use the following figure. a....Ch. 3.1 - In parts (a) and (b), use the following figure. a....Ch. 3.1 - Getting Towed The cost in dollars; to tow a car is...Ch. 3.1 - Phone Charges The monthly cost in dollars, for...Ch. 3.1 - Forensic Science The relationship between the...Ch. 3.1 - Forensic Science The relationship between the...Ch. 3.1 - Supply and Demand Suppose that the quantity...Ch. 3.1 - Supply and Demand Suppose that the quantity...Ch. 3.1 - Taxes The function T(x)=0.12(x9525)+952.50...Ch. 3.1 - Competitive balance Tax Under the 20172021 labour...Ch. 3.1 - The point at which a company’s profits equal...Ch. 3.1 - The point at which a company’s profits equal...Ch. 3.1 - Straight-line Depreciation Suppose that a company...Ch. 3.1 - Straight-line Depreciation Suppose that a company...Ch. 3.1 - Cost Function The simplest cost function is the...Ch. 3.1 - Cost function Refer to problem 49. Suppose that...Ch. 3.1 - Hooke’s law According to Hooke’s law, a linear...Ch. 3.1 - Hooke’s law The distancebetween the bottom of a...Ch. 3.1 - Challenge Problem Temperature Conversion The...Ch. 3.1 - Developing a Linear Model from Data The following...Ch. 3.1 - Which of the following functions might have the...Ch. 3.1 - Which of the following functions might have the...Ch. 3.1 - Under what circumstances is a linear function f( x...Ch. 3.1 - Explain how the graph of f( x )=mx+b can be used...Ch. 3.1 - Problems 57-60 are based on material teamed...Ch. 3.1 - Problems 57-60 are based on material teamed...Ch. 3.1 - Problems 57-60 are based on material teamed...Ch. 3.1 - Problems 57-60 are based on material teamed...Ch. 3.1 - In Problems, Complete the square for each...Ch. 3.1 - In Problems 6364, Complete the square for each...Ch. 3.1 - Find the x intercept(s) and y intercepts(s) of the...Ch. 3.1 - Find the domain of f(x)=x+2x4.Ch. 3.1 - Suppose f(x)=x23x+7. Find an equation of the...Ch. 3.1 - Use a graphing utility to graph over the...Ch. 3.2 - Plot the points ( 1,5 ),( 2,6 ),( 3,9 ),( 1,12 )...Ch. 3.2 - Find an equation of the line containing the points...Ch. 3.2 - A _____________ is used to help us to see what...Ch. 3.2 - True or False The correlation coefficient is a...Ch. 3.2 - In Problems 5-10, examine the scatter diagram and...Ch. 3.2 - In Problems 5-10, examine the scatter diagram and...Ch. 3.2 - In Problems 5-10, examine the scatter diagram and...Ch. 3.2 - In Problems 5-10, examine the scatter diagram and...Ch. 3.2 - In Problems 5-10, examine the scatter diagram and...Ch. 3.2 - In Problems 5-10, examine the scatter diagram and...Ch. 3.2 - In Problems 11-16, (a) Draw a scatter diagram. (b)...Ch. 3.2 - In Problems 11-16, (a) Draw a scatter diagram. (b)...Ch. 3.2 - In Problems 11-16, (a) Draw a scatter diagram. (b)...Ch. 3.2 - In Problems 11-16, (a) Draw a scatter diagram. (b)...Ch. 3.2 - In Problems 11-16, (a) Draw a scatter diagram. (b)...Ch. 3.2 - In Problems 11-16, (a) Draw a scatter diagram. (b)...Ch. 3.2 - Candy The following data represent the weight (in...Ch. 3.2 - Tornadoes The following data represent the width...Ch. 3.2 - Video Games and Grade-Point Average Professor...Ch. 3.2 - Hurricanes The following data represent the...Ch. 3.2 - Maternal Age versus Down Syndrome A biologist...Ch. 3.2 - U.S. Advertising The following data represents the...Ch. 3.2 - Find the line of best fit for the ordered pairs (...Ch. 3.2 - What does a correlation coefficient of 0 imply?Ch. 3.2 - Explain why it does not make sense to interpret...Ch. 3.2 - Refer to Problem 19. Solve G( h )=0 . Provide an...Ch. 3.2 - Find an equation for the line containing the...Ch. 3.2 - Find the domain of f( x )= x1 x 2 25 .Ch. 3.2 - For f(x)=5x8 and g(x)= x 2 3x+4 , find (gf)(x) .Ch. 3.2 - Write the function whose graph is the graph of y=...Ch. 3.2 - Solve: x24x=3Ch. 3.2 - Solve. Write the answer in interval notation....Ch. 3.2 - Determine algebraically whether the function...Ch. 3.2 - Find the x intercept(s) and y intercept(s) of the...Ch. 3.2 - Rationalize the numerator:
Ch. 3.2 - Write 4x(2+x)12+3(2+x)12,x2, as a single quotient...Ch. 3.3 - List the intercepts of the equation y= x 2 9 ....Ch. 3.3 - Prob. 2AYUCh. 3.3 - To complete the square of x 2 5x , you add the...Ch. 3.3 - To graph y= (x4) 2 you shift the graph of y= x 2...Ch. 3.3 - Find the discriminant of . Then identify the...Ch. 3.3 - Prob. 6AYUCh. 3.3 - The graph of a quadratic function is called a(n)...Ch. 3.3 - The vertical line passing through the vertex of a...Ch. 3.3 - The x-coordinate of the vertex of f( x )=a x 2...Ch. 3.3 - True or False The graph of f( x )=2 x 2 +3x4 opens...Ch. 3.3 - True or False The y-coordinate of the vertex of f(...Ch. 3.3 - True or False If the discriminant b 2 4ac=0 , the...Ch. 3.3 - If b 2 4ac0 , which of the following conclusions...Ch. 3.3 - If the graph of f( x )=a x 2 +bx+c,a0 , has a...Ch. 3.3 - In Problems 13-20, match each graph to one the...Ch. 3.3 - In Problems 13-20, match each graph to one the...Ch. 3.3 - In Problems 13-20, match each graph to one the...Ch. 3.3 - In Problems 13-20, match each graph to one the...Ch. 3.3 - In Problems 13-20, match each graph to one the...Ch. 3.3 - In Problems 13-20, match each graph to one the...Ch. 3.3 - In Problems 13-20, match each graph to one the...Ch. 3.3 - In Problems 13-20, match each graph to one the...Ch. 3.3 - In Problems, find the vertex and axis of symmetry...Ch. 3.3 - In Problems 2330, (a) find the vertex and axis of...Ch. 3.3 - In Problems 2330, (a) find the vertex and axis of...Ch. 3.3 - In Problems 2330, (a) find the vertex and axis of...Ch. 3.3 - In Problems 2330, (a) find the vertex and axis of...Ch. 3.3 - In Problems, find the vertex and axis of symmetry...Ch. 3.3 - In Problems, find the vertex and axis of symmetry...Ch. 3.3 - In Problems 2330, (a) find the vertex and axis of...Ch. 3.3 - In Problems 21-32, graph the function f by...Ch. 3.3 - In Problems 21-32, graph the function f by...Ch. 3.3 - In Problems 21-32, graph the function f by...Ch. 3.3 - In Problems 21-32, graph the function f by...Ch. 3.3 - In Problems 21-32, graph the function f by...Ch. 3.3 - In Problems 21-32, graph the function f by...Ch. 3.3 - In Problems 21-32, graph the function f by...Ch. 3.3 - In Problems 21-32, graph the function f by...Ch. 3.3 - In Problems 21-32, graph the function f by...Ch. 3.3 - In Problems 21-32, graph the function f by...Ch. 3.3 - In Problems 21-32, graph the function f by...Ch. 3.3 - In Problems 21-32, graph the function f by...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 49-54, determine the quadratic...Ch. 3.3 - In Problems 49-54, determine the quadratic...Ch. 3.3 - In Problems 49-54, determine the quadratic...Ch. 3.3 - In Problems 49-54, determine the quadratic...Ch. 3.3 - In Problems 49-54, determine the quadratic...Ch. 3.3 - In Problems 49-54, determine the quadratic...Ch. 3.3 - In Problems 6572, determine, without graphing,...Ch. 3.3 - In Problems 55-62, determine, without graphing,...Ch. 3.3 - In Problems 55-62, determine, without graphing,...Ch. 3.3 - In Problems 55-62, determine, without graphing,...Ch. 3.3 - In Problems, determine, without graphing, whether...Ch. 3.3 - In Problems 55-62, determine, without graphing,...Ch. 3.3 - In Problems, determine, without graphing, whether...Ch. 3.3 - In Problems 55-62, determine, without graphing,...Ch. 3.3 - The graph of the function f( x )=a x 2 +bx+c has...Ch. 3.3 - The graph of the function f(x)=a x 2 +bx+c has...Ch. 3.3 - In Problems 77-82, for the given functions fandg ,...Ch. 3.3 - In Problems 77-82, for the given functions fandg ,...Ch. 3.3 - In Problems 77-82, for the given functions fandg ,...Ch. 3.3 - In Problems 77-82, for the given functions fandg ,...Ch. 3.3 - In Problems 77-82, for the given functions fandg ,...Ch. 3.3 - In Problems 77-82, for the given functions fandg ,...Ch. 3.3 - Answer Problems 83 and 84 using the following: A...Ch. 3.3 - Answer Problems 83 and 84 using the following: A...Ch. 3.3 - Suppose that f(x)= x 2 +4x21 . (a) What is the...Ch. 3.3 - Suppose that f( x )= x 2 +2x8 . (a) What is the...Ch. 3.3 - Analyzing the Motion of a Projectile A projectile...Ch. 3.3 - Analyzing the Motion of a Projectile A projectile...Ch. 3.3 - Maximizing Revenue Suppose that the manufacturer...Ch. 3.3 - Maximizing Revenue A lawn mower manufacturer has...Ch. 3.3 - Minimizing Marginal Cost The marginal cost of a...Ch. 3.3 - Minimizing Marginal Cost (See Problem 91.) The...Ch. 3.3 - Business The monthly revenue R achieved by selling...Ch. 3.3 - Business The daily revenue R achieved by selling x...Ch. 3.3 - Stopping Distance An accepted relationship between...Ch. 3.3 - Birth Rate of Unmarried Women In the United...Ch. 3.3 - Chemical Reactions A self-catalytic chemical...Ch. 3.3 - Mixed Practice Find the distance from the vertex...Ch. 3.3 - Mixed Practice Find the distance from the vertex...Ch. 3.3 - Prob. 98AYUCh. 3.3 - Prob. 99AYUCh. 3.3 - Prob. 100AYUCh. 3.3 - Prob. 101AYUCh. 3.3 - Prob. 102AYUCh. 3.3 - Make up a quadratic function that opens down and...Ch. 3.3 - Prob. 104AYUCh. 3.3 - Prob. 105AYUCh. 3.3 - Prob. 106AYUCh. 3.3 - Prob. 107AYUCh. 3.3 - Prob. 108AYUCh. 3.3 - What are the possibilities for the number of times...Ch. 3.3 - Prob. 110AYUCh. 3.3 - Prob. 111AYUCh. 3.3 - Prob. 112AYUCh. 3.3 - Prob. 113AYUCh. 3.3 - Prob. 114AYUCh. 3.3 - State the domain and range of the relation given...Ch. 3.3 - Prob. 116AYUCh. 3.3 - Prob. 117AYUCh. 3.3 - Prob. 118AYUCh. 3.3 - Prob. 119AYUCh. 3.4 - Translate the following sentence into a...Ch. 3.4 - Use a graphing utility to find the line of best...Ch. 3.4 - Maximizing Revenue The price p(in dollars) and the...Ch. 3.4 - Maximizing Revenue The price p(in dollars) and the...Ch. 3.4 - Maximizing Revenue The price p (in dollars) and...Ch. 3.4 - Maximizing Revenue The price p (in dollars) and...Ch. 3.4 - Enclosing a Rectangular Field David has 400 yards...Ch. 3.4 - Enclosing a Rectangular Field Beth has 3000 feet...Ch. 3.4 - Enclosing a Rectangular Field with a Fence A...Ch. 3.4 - Enclosing a Rectangular Field with a Fence A...Ch. 3.4 - Suspension Bridge A suspension bridge with weight...Ch. 3.4 - Architecture A parabolic arch has a span of 120...Ch. 3.4 - Constructing Rain Gutters A rain gutter is to be...Ch. 3.4 - Norman Windows A Norman window has the shape of a...Ch. 3.4 - Constructing a Stadium A track-and-field playing...Ch. 3.4 - Architecture A special window has the shape of a...Ch. 3.4 - Life Cycle Hypothesis An individuals income varies...Ch. 3.4 - Height of a Rail A shot-putter throws a hall at an...Ch. 3.4 - Mixed Practice Which Model? The following data...Ch. 3.4 - Which Model? A cricket makes a chirping noise by...Ch. 3.4 - Mixed Practice Which Model? The following data...Ch. 3.4 - Prob. 22AYUCh. 3.4 - Prob. 23AYUCh. 3.4 - Prob. 24AYUCh. 3.4 - Prob. 25AYUCh. 3.4 - Prob. 26AYUCh. 3.4 - Prob. 27AYUCh. 3.4 - Prob. 28AYUCh. 3.4 - Prob. 29AYUCh. 3.4 - Prob. 30AYUCh. 3.4 - Prob. 31AYUCh. 3.4 - Prob. 32AYUCh. 3.4 - Prob. 33AYUCh. 3.4 - Prob. 34AYUCh. 3.4 - Prob. 35AYUCh. 3.4 - Prob. 36AYUCh. 3.4 - Prob. 37AYUCh. 3.5 - Solve the inequality 3x27 .Ch. 3.5 - Write (2,7] using inequality notation.Ch. 3.5 - (a) f( x )0 (b) f( x )0Ch. 3.5 - (a) g( x )0 (b) g( x )0Ch. 3.5 - (a) g( x )f( x ) (b) f( x )g( x )Ch. 3.5 - (a) f( x )g( x ) (b) f( x )g( x )Ch. 3.5 - x 2 3x100Ch. 3.5 - x 2 +3x100Ch. 3.5 - x 2 4x0Ch. 3.5 - x 2 +8x0Ch. 3.5 - x 2 90Ch. 3.5 - x 2 10Ch. 3.5 - x 2 +x12Ch. 3.5 - x 2 +7x12Ch. 3.5 - 2 x 2 5x+3Ch. 3.5 - 6 x 2 6+5xCh. 3.5 - x 2 x+10Ch. 3.5 - x 2 +2x+40Ch. 3.5 - 4 x 2 +96xCh. 3.5 - 25 x 2 +1640xCh. 3.5 - 6( x 2 1 )5xCh. 3.5 - 2( 2 x 2 3x )9Ch. 3.5 - In Problems 25-32, use the given functions f and g...Ch. 3.5 - In Problems 25-32, use the given functions f and g...Ch. 3.5 - In Problems 25-32, use the given functions f and g...Ch. 3.5 - In Problems 25-32, use the given functions f and g...Ch. 3.5 - In Problems 25-32, use the given functions f and g...Ch. 3.5 - In Problems 25-32, use the given functions f and g...Ch. 3.5 - In Problems 25-32, use the given functions f and g...Ch. 3.5 - In Problems 25-32, use the given functions f and g...Ch. 3.5 - What is the domain of the function f( x )= x 2 16...Ch. 3.5 - What is the domain of the function f( x )= x3 x 2...Ch. 3.5 - Physics A ball is thrown vertically upward with an...Ch. 3.5 - Physics A ball is thrown vertically upward with an...Ch. 3.5 - Revenue Suppose that the manufacturer of a gas...Ch. 3.5 - Revenue The John Deere company has found that the...Ch. 3.5 - Artillery A projectile Fired from the point ( 0,0...Ch. 3.5 - Runaway Car Using Hooke's Law, we can show that...Ch. 3.5 - Show that the inequality ( x4 ) 2 0 has exactly...Ch. 3.5 - Show that the inequality ( x2 ) 2 0 has one real...Ch. 3.5 - Explain why the inequality x 2 +x+10 has all real...Ch. 3.5 - Explain why the inequality x 2 x+10 has the empty...Ch. 3.5 - Explain the circumstances under which the...Ch. 3.5 - Determine the domain of f( x )= 102x .Ch. 3.5 - Determine algebraically whether f( x )= x x 2 +9...Ch. 3.5 - Consider the linear function f( x )= 2 3 x6 . (a)...Ch. 3.5 - Determine whether the graphs ofandare parallel,...Ch. 3.5 - Find the zeros of f(x)=x2+6x8.Ch. 3.5 - Find the intercepts of the graph of.
Ch. 3.5 - In Problems 50 and 51, if f(x)=x2+2x7 and...Ch. 3.5 - In Problemsand, ifand, find:
Ch. 3.5 - Find the difference quotient of f: f(x)=3x25xCh. 3.5 - Simplify:
Ch. 3 - In Problems 1-3: (a) Determine the slope and...Ch. 3 - In Problems:
Find the slope and-intercept of each...Ch. 3 - In Problems 1-3: (a) Determine the slope and...Ch. 3 - In Problems 4 and 5, determine whether the...Ch. 3 - In Problems 4 and 5, determine whether the...Ch. 3 - In Problems, graph each quadratic function using...Ch. 3 - In Problems 6-8, graph each quadratic function...Ch. 3 - In Problems, graph each quadratic function using...Ch. 3 - In Problems 6-8, graph each quadratic function...Ch. 3 - In Problems 913, (a) graph each quadratic function...Ch. 3 - In Problems 9-14, (a) graph each quadratic...Ch. 3 - In Problems 913, (a) graph each quadratic function...Ch. 3 - In Problems 9-14, (a) graph each quadratic...Ch. 3 - In Problems 15-17, determine whether the given...Ch. 3 - In Problems 15-17, determine whether the given...Ch. 3 - In Problems, determine whether the given quadratic...Ch. 3 - In Problems 18-19, solve each quadratic...Ch. 3 - In Problems 18-19, solve each quadratic...Ch. 3 - In Problems 19 and 20, find the quadratic function...Ch. 3 - 20. In Problems 20 and 21, find the quadratic...Ch. 3 - 22. Sales Commissions Bill has just been offered a...Ch. 3 - Demand Equation The price(in dollars) and the...Ch. 3 - Landscaping A landscape engineer has 200 feet of...Ch. 3 - 24. Enclosing the Most Area with a Fence A farmer...Ch. 3 - Architecture A special window in the shape of a...Ch. 3 - 25. Minimizing Marginal Cost Callaway Golf Company...Ch. 3 - 26. Maximizing Area A rectangle has one vertex on...Ch. 3 - 27. Parabolic Arch Bridge A horizontal bridge is...Ch. 3 - 28. Bono Length Research performed at NASA, led by...Ch. 3 - 29. Advertising A small manufacturing firm...Ch. 3 - For the linear function f( x )=4x+3 , a. Find the...Ch. 3 - In Problems 2 and 3, find the intercepts, if any,...Ch. 3 - In Problemsand, find the intercepts, if any, of...Ch. 3 - Graph f(x)= (x3) 2 2 using transformations.Ch. 3 - Supposeand.
Solve
Graph each function and label...Ch. 3 - Consider the quadratic function
Is the graph...Ch. 3 - Determine whether f( x )=-2 x 2 +12x+3 has a...Ch. 3 - Solve, x 2 10x+240 .Ch. 3 - The weekly rental cost of a 20-foot recreational...Ch. 3 - Maximizing Revenue The price p(in dollars) and the...Ch. 3 - Find the distance between the points P=( 1,3 ) and...Ch. 3 - Which of the following points are on the graph of,...Ch. 3 - Solve the inequality 5x+30 and graph the solution...Ch. 3 - Find the equation of the line containing the...Ch. 3 - Find the equation of the line perpendicular to the...Ch. 3 - Graph the equation x 2 + y 2 4x+8y5=0 .Ch. 3 - Does the following relation represent a function?...Ch. 3 - For the function f defined by f( x )= x 2 4x+1 ,...Ch. 3 - Find the domain of h(z)= 3z1 6z7 .Ch. 3 - Is the following graph the graph of a function?Ch. 3 - Consider the function f(x)= x x+4 . a. Is the...Ch. 3 - Is the function f(x)= x 2 2x+1 even, odd, or...Ch. 3 - Approximate the local maximum values and local...Ch. 3 - If f(x)=3x+5 and g(x)=2x+1 , a. Solve f(x)=g( x )...Ch. 3 - For the graph of the function f , a. Find the...
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- A chemical manufacturing plant can produce x units of chemical Z given p units of chemical P and 7 units of chemical R, where: z = 140p0.6,0.4 Chemical P costs $300 a unit and chemical R costs $1,500 a unit. The company wants to produce as many units of chemical Z as possible with a total budget of $187,500. A) How many units each chemical (P and R) should be "purchased" to maximize production of chemical Z subject to the budgetary constraint? Units of chemical P, p = Units of chemical R, r = B) What is the maximum number of units of chemical Z under the given budgetary conditions? (Round your answer to the nearest whole unit.) Max production, z= unitsarrow_forwardA firm manufactures a commodity at two different factories, Factory X and Factory Y. The total cost (in dollars) of manufacturing depends on the quantities, and y produced at each factory, respectively, and is expressed by the joint cost function: C(x, y) = x² + xy +4y²+400 A) If the company's objective is to produce 1,900 units per month while minimizing the total monthly cost of production, how many units should be produced at each factory? (Round your answer to whole units, i.e. no decimal places.) To minimize costs, the company should produce: units at Factory X and units at Factory Y B) For this combination of units, their minimal costs will be enter any commas in your answer.) Question Help: Video dollars. (Do notarrow_forwarduse Lagrange multipliers to solvearrow_forward
- Suppose a Cobb-Douglas Production function is given by the following: P(L,K)=80L0.75 K-0.25 where L is units of labor, K is units of capital, and P(L, K) is total units that can be produced with this labor/capital combination. Suppose each unit of labor costs $400 and each unit of capital costs $1,600. Further suppose a total of $384,000 is available to be invested in labor and capital (combined). A) How many units of labor and capital should be "purchased" to maximize production subject to your budgetary constraint? Units of labor, L = Units of capital, K = B) What is the maximum number of units of production under the given budgetary conditions? (Round your answer to the nearest whole unit.) Max production = unitsarrow_forwardSuppose a Cobb-Douglas Production function is given by the function: P(L, K) = 7L0.0 K0.4 Furthemore, the cost function for a facility is given by the function: C(L, K) = 100L +400K Suppose the monthly production goal of this facility is to produce 15,000 items. In this problem, we will assume L represents units of labor invested and K represents units of capital invested, and that you can invest in tenths of units for each of these. What allocation of labor and capital will minimize total production Costs? Units of Labor L = Units of Capital K = (Show your answer is exactly 1 decimal place) (Show your answer is exactly 1 decimal place) Also, what is the minimal cost to produce 15,000 units? (Use your rounded values for L and K from above to answer this question.) The minimal cost to produce 15,000 units is $ Hint: 1. Your constraint equation involves the Cobb Douglas Production function, not the Cost function. 2. When finding a relationship between L and K in your system of equations,…arrow_forwardFind the absolute maximum and minimum of f(x, y) = x + y within the domain x² + y² ≤ 4. Please show your answers to at least 4 decimal places. Enter DNE if the value does not exist. 1. Absolute minimum of f(x, y) isarrow_forward
- Suppose that one factory inputs its goods from two different plants, A and B, with different costs, 3 and 7 each respective. And suppose the price function in the market is decided as p(x, y) = 100 - x - y where I and y are the demand functions and 0 < x,y. Then as x = y = the factory can attain the maximum profit,arrow_forwardEvaluate the following integrals, showing all your workingarrow_forwardConsider the function f(x) = 2x³-4x2-x+1. (a) Without doing a sketch, show that the cubic equation has at least one solution on the interval [0,1]. Use a theorem discussed in lectures, or see Section 1.8 of Calculus (7th ed) by Stewart. Ensure that the conditions of the theorem are satisfied (include this in your solution) (b) Now, by sketching the cubic (by hand or by computer), you should see that there is, in fact, exactly one zero in the interval [0,1]. Use Newton's method to find this zero accurate to 3 decimal places. You should include a sketch of the cubic, Newton's iteration formula, and the list of iterates. [Use a computer if possible, e.g., a spreadsheet or MatLab.]arrow_forward
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