A wheat farmer is converting to corn because he believes that corna more lucrative crop. It is not feasible for him to convert all his acreage to corn at once. He is farming 500 acres ofcorn in the current year and is increasing that number by 20 acres per yearhe becomes more experienced in growing corn, his output increases. He currently harvests 130 bushels ofcorn per acre, but the yield is increasing by 5 bushels per acre per year. When both the increasing acreage and the increasing yield are considered, how rapidly is the total number ofbushels of corn currently increasing?x bushels per year5300

Let f(n) denote the number of acres devoted to corn in year n. We have f(n)=500+20n.Let g(n) denote…

Answered: A wheat farmer is converting to corn…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Brawdy Plastics, Inc., produces plastic seat belt retainers for General Motors at the Brawdy Plastics plant in Buffalo, New York. After final assembly and painting, the parts are placed on a conveyor belt that moves the parts past a final inspection station. How fast the parts move past the final inspection station depends upon the line speed of the conveyor belt (feet per minute). Although faster line speeds are desirable, management is concerned that increasing the line speed too much may not provide enough time for inspectors to identify which parts are actually defective. To test this theory, Brawdy Plastics conducted an experiment in which the same batch of parts, with a known number of defective parts, was inspected using a variety of line speeds. The following data were collected. Line Number of Defective Parts Found Speed 20 24 20 20 30 19 30 16 40 14 40 18 50 14 50 11 (a) Develop a scatter diagram with the line speed as the independent variable. 25 20 20 20 15 15 15 ● 15 10 10…
A car's cooling system has a capacity of 30 quarts. Initially, the system contains a mixture of 6 quarts of antifreeze and 15 quarts of water. Water runs into the system at the rate of 1 gallon per minute, then the homogeneous mixture runs out at the same rate. How much antifreeze is in the system at the end of 6 minutes?
Please answer this. Thanks!
A group of scientists studied the effect of a chemical on various strains of bacteria. Bacteria A started with 12000 cells and decreased at a constant rate of 3000 cells per hour after the chemical was applied. Strain B started with 4000 cells and decreased at a constant rate of 2000 cells per hour after the chemical was applied. When will the strains have the same number of cells?
Apple Company creates new plan to decide the quantity of mobile phone to be produced. There are 3 Phone Types: IPhone 6, IPhone 5 and IPhone 7. Knowing that the profit per unit of each IPhone 6 is $80, IPhone 5 : $60, and IPhone 7 : $20. Market research has indicated that the maximum demand is 200 for IPhone 5. IPhone 6 has to be more than 30% of IPhone 7. The maximum production availability for all mobile phones is 720.The number of work hours available is at most 500 hours. An IPhone 6 requires 26 hours, an IPhone 5 requires 16 hours, and an IPhone 7 requires 18 hours. Formulate this as a linear programming problem.
Based on the model, what is the difference in predicted amounts of milk producedbetween a cow of 5 years and a cow of 10 years? (A) (B) (C) (D) (E) A cow of 5 years is predicted to produce 5.5 fewer gallons per week.A cow of 5 years is predicted to produce 5.5 more gallons per week.A cow of 5 years is predicted to produce 1.1 fewer gallons per week.A cow of 5 years is predicted to produce 1.1 more gallons per week.A cow of 5 years and a cow of 10 years are both predicted to produce 40.8 gallons per week.
The Transit Authority (TA)in a metropolitan area operates a subway line that currently carries an average of 6000 passengers per day commuting between the suburbs and downtown. The fare now is $3.00 per ride and the board of the TA is considering raising its price by $0.50 to generate a larger revenue. A study reveals that for each $0.50 increase in fare, the ridership will be reduced by an average of 1000 passengers per day. Using this study, the board determines that, to get maximum profit, the price of the ticket should remain at $3.00. Is this correct? Explain why or why not.
A company produces two types of hand soaps: a solid and a liquid soap. The cost of production for a solid soap is 10 cents per soap and 20 cents for the liquid soap. The company developed a model that predicts how many units x1 (of the solid soap), and x2 (of the liquid soap) they will sell per month. According to the model, the amount of units sold depends on the prices p1,p2 (in dollars) of solid and liquid soap through the equations ( see attached for equation) Set up a function to describe how the total profit (revenue - costs) depends on the unit prices p1 and p2.
Brawdy Plastics, Inc., produces plastic seat belt retainers for General Motors at the Brawdy Plastics plant in Buffalo, New York. After final assembly and painting, the parts are placed on a conveyor belt that moves the parts past a final inspection station. How fast the parts move past the final inspection station depends upon the line speed of the conveyor belt (feet per minute). Although faster line speeds are desirable, management is concerned that increasing the line speed too much may not provide enough time for inspectors to identify which parts are actually defective. To test this theory, Brawdy Plastics conducted an experiment in which the same batch of parts, with a known number of defective parts, was inspected using a variety of line speeds. The following data were collected. LineSpeed Number ofDefectiveParts Found 20 23 20 21 30 19 30 15 40 16 40 18 50 14 50 10 (a) Develop a scatter diagram with the line speed as the independent variable. A…
Two connected tanks, each with a capacity of 50 liters, contain brine (saltwater). Initially, the first tank contains 18 liters of brine with a salt concentration of 3 grams per liter and the second contains 17 liters of brine with a salt concentration of 2 grams per liter. At t = 0 brine with a salt concentration of 6 grams per liter flows into the first tank at 8 liters per hour. Well-stirred brine flows from the first tank into the second at 7 liters per hour, from the second into the first at 5 liters per hour, from the first into a drain at 4 liters per hour, and from the second into a drain at 3 liters per hour. (a) Determine the volume (liters) of brine in each tank as a function of time.(b) Give an initial-value problem that governs the amount (grams) of salt in eachtank as a function of time.(c) Give the interval of definition for the solution of this initial-value problem.
Jenck's Homemade Ice Cream, LLC is planning its production for next week. As there is a current shortage of fresh milk and one of the mixing machines is broken, demand for chocolate chocolate-chip ice cream and chocolate peanut-butter ice cream continues to outpace the company's production capacities. The mixing machines will be available for only for only 158.6 hours, and only 17500 gallons of high grade milk will be available. One hundred gallons of chocolate chocolate-chip requires 0.6 hour of mixing and 75 gallons of milk. One hundred gallons of chocolate peanut-butter ice cream requires 0.8 hour of mixing and 80 gallons of milk. If company earns a profit of $115.00 per hundred gallons of chocolate chocolate-chip and $130.00 per hundred gallons of chocolate peanut-butter, how many gallons of each ice cream should company produce next week to maximize profit? How much profit will result? (Use x for hundred gallons of chocolate chocolate-chip and y for hundred gallons of chocolate…
Brawdy Plastics, Inc., produces plastic seat belt retainers for General Motors at the Brawdy Plastics plant in Buffalo, New York. After final assembly and painting, the parts are placed on a conveyor belt that moves the parts past a final inspection station. How fast the parts move past the final inspection station depends upon the line speed of the conveyor belt (feet per minute). Although faster line speeds are desirable, management is concerned that increasing the line speed too much may not provide enough time for inspectors to identify which parts are actually defective. To test this theory, Brawdy Plasticsm conducted an experiment in which the same batch of parts, with a known number of defective parts, was inspected using a variety of line speeds. The following data were collected. a. Develop a scatter diagram with the line speed as the independent variable. b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables? c. Use…

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