Concept explainers
(a)
The equation models the costs of producing x pair of item-S.
The cost function model is
Given:
The annual cost C of making x pairs of items is
Concept Used:
The cost function is made up of two quantity, one a variable quantity that depends on numbers of productions and other is constant, that is fixed.
Calculation:
If
Thus, the equation models of the costs of producing x pair of item is:
Conclusion:
The cost function model is
(b)
The equation models the revenue of selling x pair of item-S.
The equation models the revenue of selling x pair of item-S is
Given:
The annual cost C of making x pairs of items is
Concept Used:
The revenue is the amount generated by selling the item.
Calculation:
The item-C is sold at
Hence, the equation models the revenue of selling x pair of item-S is:
Conclusion:
The equation models the revenue of selling x pair of item-S is
(c)
The numbers of pairs to be produce and sold in order to break even.
The graph of equation model cost and revenue intersecting at break-even.
Given:
The annual cost C of making x pairs of items is
Concept Used:
The break-even point arrives when cost and revenue are equal.
Calculation:
The cost and revenue function for x pairs of items is
If x is the numbers of pairs in order to break even, then
Solve
Hence, the numbers of pairs to be produce and sold in order to break even is
Conclusion:
The numbers of pairs to be produce and sold in order to break even is
(d)
The graph of equation that models the cost and revenue and interprets the break-even point.
The numbers of pairs to be produce and sold in order to break even is
Given:
The annual cost C of making x pairs of items is
Concept Used:
Plot the points on graph obtained by choosing different values of x and join the points.
Calculation:
The cost function is
To graph the functions, compute the values for different values of x :
The points are plotted as follows:
Interpretation:
The graph of two equation of cost and revenue model intersect at
Conclusion:
The graph of equation model cost and revenue intersecting at break-even.
Chapter 1 Solutions
PRECALCULUS:...COMMON CORE ED.-W/ACCESS
- 39. (a) Show that Σeak converges for each α > 0. (b) Show that keak converges for each a > 0. k=0 (c) Show that, more generally, Σk"eak converges for each k=0 nonnegative integer n and each a > 0.arrow_forward#3 Find the derivative y' = of the following functions, using the derivative rules: dx a) y-Cos 6x b) y=x-Sin4x c) y=x-Cos3x d) y=x-R CD-X:-:TCH :D:D:D - Sin f) Sin(x²) (9) Tan (x³)arrow_forwardmate hat is the largest area that can be en 18 For the function y=x³-3x² - 1, use derivatives to: (a) determine the intervals of increase and decrease. (b) determine the local (relative) maxima and minima. (c) determine the intervals of concavity. (d) determine the points of inflection. b) (e) sketch the graph with the above information indicated on the graph.arrow_forward
- use L'Hopital Rule to evaluate the following. a) 4x3 +10x2 23009׳-9 943-9 b) hm 3-84 хто бу+2 < xan x-30650)arrow_forwardEvaluate the next integralarrow_forward1. For each of the following, find the critical numbers of f, the intervals on which f is increasing or decreasing, and the relative maximum and minimum values of f. (a) f(x) = x² - 2x²+3 (b) f(x) = (x+1)5-5x-2 (c) f(x) = x2 x-9 2. For each of the following, find the intervals on which f is concave upward or downward and the inflection points of f. (a) f(x) = x - 2x²+3 (b) g(x) = x³- x (c) f(x)=x-6x3 + x-8 3. Find the relative maximum and minimum values of the following functions by using the Second Derivative Test. (a) f(x)=1+3x² - 2x3 (b) g(x) = 2x3 + 3x² - 12x-4arrow_forward
- Find the Soultion to the following dy differential equation using Fourier in transforms: = , хуо, ухо according to the terms: lim u(x,y) = 0 x18 lim 4x (x,y) = 0 x14 2 u (x, 0) = =\u(o,y) = -y لوarrow_forwardCan you solve question 3,4,5 and 6 for this questionarrow_forwardwater at a rate of 2 m³/min. of the water height in this tank? 16) A box with a square base and an open top must have a volume of 256 cubic inches. Find the dimensions of the box that will minimize the amount of material used (the surface area). 17) A farmer wishes toarrow_forward
- #14 Sand pours from a chute and forms a conical pile whose height is always equal to its base diameter. The height o the pile increases at a rate of 5 feet/hour. Find the rate of change of the volume of the sand in the conical pile when the height of the pile is 4 feet.arrow_forward(d)(65in(x)-5 cos(x) dx mins by 5x-2x² 3x+1 dx -dx 20 Evaluate each the following indefinite integralsarrow_forward19 Evaluate each the following definite integrals: a) લ b) (+3) 6) (2-2)(+33) dxarrow_forward
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning





