It costs the American Automobile Company $8,000 to produce each automobile, and fixed costs (rent and other expenses that do not depend on the amount of production) are $15,000 per week.  The company’s price function is px=20,000-60x, where p is the price at which exactly x cars will be sold. a)  How many cars should be produced each week to maximize profit? b)  For what price should they be sold? c)  What is the company’s maximum profit?

Q: A commodity has a demand function modeled by p=36-4x, and a total cost function modeled by C=2x^2…

A:

Q: A manufacturer of lighting fixtures has daily production costs of  C = 800 − 50x + 0.25x2,  where C…

A: For finding minimum of any function take derivative and equate to zero.

Q: A firm’s revenue after selling q items is given by R(q) = 2q3 +36q while the firm’s costs after making…

A: R(q) = 2q3 +36qC(q) = 3q2 −10Profit, P(q) = R(q) - C(q) = 2q3 +36q - (3q2 −10) = 2q3 - 3q2 +…

Q: Use Lagrange multipliers to find the maximum production level when the total cost of labor (at $112…

A:

Q: If the total revenue function for a computer is R(x) = 1200x – 32x2 – x3, find the level of sales,…

A: Let's find.

Q: Assume that it costs a manufacturer approximately C(x) = 800,000 + 340x + 0.0005x2 dollars to…

A: In this question, optimization technique is used. Optimization Technique using maxima and minima The…

Q: An automobile dealer can sell 12 cares per day at a price of $15,000. He estimates that for each…

A: An automobile dealer can sell 12 cares per day at a price of $15,000. He estimates that for each…

Q: Find the price that will maximize profit for the demand and cost functions, where p is the price, x…

A: given Demand Function  p = 74 − 0.1x cost=29x+600

Q: An apple grower finds that if he plants 80 trees per acre, each tree will yield 26 bushels of fruit.…

A:

Q: steel

A: Please refer to the image below

Q: Find the price that will maximize profit for the demand and cost functions, where p is the price, x…

A: Given query is to find the price that will maximize the profit.

Q: (b) The revenue R(x, y) that Scoot Airline collects from selling its normal seats and premium seats…

A:

Q: A manufacturer supplies refrigerators to two stores, A and B. The manager esti- mates that if x…

A:

Q: The manufacturer of a electronic tablet has found that the revenue R (in dollars) is R(p) = -5p2 +…

A: We are given the revenue equation as R(p) = -5p2 + 1180p. Here, we need to the maximum revenue. Now,…

Q: If the total revenue function for a computer is R(x) = 1800x – 23x2 - x³, find the level of sales,…

A:

Q: Find the maximum profit and the number of units that must be produced and sold in order to achieve…

A:

Q: Use Lagrange multipliers to find the maximum production level when the total cost of labor (at $113…

A:

Q: A company making Espresso machines has a demand price that can be modeled by p=500-0.5q^2 and the…

A: Given that: demand price is modeled by p=500-0.5q^2 the total cost is modeled by C=50q+40 To Find:…

Q: f in a monopoly market the demand for a product is p=1600-x and the revenue is R=px, where x is the…

A: Given,  The demand for a product is  p=1600-x Revenue is R = px  where x is the number of units sold…

Q: A POP bookstore sells a drawing book for RM1.50 each. The daily cost function is estimated to be…

A:

Q: Assume that each small sandwich uses 4 inches of bread and 3 ounces of meat, and that each large…

A: Given:  The given information is summarized in following table:   Small Large   Bread 4 in 12…

Q: An independent political candidate wants to run both TV and radio advertisements. Suppose that each…

A:

Q: If a consumer has an income of $200, the price of X is $5, and the price of Y is $10, what is the…

A: We will solve the following

Q: A plant can manufacture 40 tennis racket per day for a total daily cost of $3,500 and 22 tennis…

A: Given: A plant can manufacture 40 tennis racket per day for a total daily cost of $3,500 and 22…

Q: Find the price that will maximize profit for the demand and cost functions, where p is the price, x…

A:

Q: Find the price that will maximize profit for the demand and cost functions, where p is the price, x…

A:

Q: If the total revenue function for a computer is R(x) = 2600x − 11x^2 − x^3, find the level of sales,…

A:

Q: If the total revenue function for a computer is  R(x) = 3000x − 5x2 − x3,  find the level of sales,…

A:

Q: Two vertical poles, one 16 ft high and the other 24 ft high, stand 30 feet apart on a flat field. A…

A:

Q: A vegetable farmer in Bulacan ships 1,000 baskets of vegetables on a freight car daily to  Sampaloc…

A:

Q: The estimated monthly profit (in dollars) realizable by Cannon Precision Instruments for…

A: given that P(x)=-0.02x2+92x-109000

Q: The manager of a 100 unit apartment complex is trying to decide what to charge for rent. Experience…

A:

Q: The demand for monorail service in the three districts of Utarek on Mars can be approximated by q =…

A: Given that: The demand for monorail service in the three districts of Utarek on Mars can be…

Q: A company operates two plants which manufacture the same item and whose total cost functions are C1…

A: As we know Revenue is price multiplied by the demand so

Q: Bubba, a farmer, wants to fence-in a three-sided area next to his barn, using the side of the barn…

A:

Q: a cost function of C=16x2−133x+9878C=16x2-133x+9878, where CC is the cost in dollars and xx is the…

A: Given query is to find the units to minimize the cost.

Q: Find the price that will maximize profit for the demand and cost functions, where p is the price, x…

A:

Q: An oil- producing country can sell 7 million barrels of oil a day at price of $90 per barrel. If…

A:

Q: A retail outlet sells two type of lawn mowers, the prices of which are p1 and p2. Find p1 and p2 so…

A:

Q: contains 90 IU of vitamin A, 3 mg of vitamin B1, and 5 mg of vitamin C, and pill 2, which contains…

A: Since you have asked multiple questions,we will solve the first question for you.If you want any…

Q: Assume that it costs a manufacturer approximately C(x) = 1,058,000 + 340x + 0.0005x2 dollars to…

A: C(x) = 1,058,000 + 340x + 0.0005x2a)Minimum average cost isC ¯(x)=c(x)x=1058000+340x+0.0005x2x…

Q: A company operates two plants which manufacture the same item and whose total cost functions are C1…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: A fruit farmer finds that if she plants 50 trees per acre, each tree will yield 75 boxes of fruit…

A: I am attaching image so that you understand each and every step.

Q: A home gardener estimates that 19 apple trees will have an average yield of 147 apples per tree. But…

A: Total  number of apple  trees=x+19GIVEN:Additional tree planted the yield will decrease by three…

Q: you sell each Quebee at the Breakeven Price, what is your maximum profit? What is your maximum loss

A: In this question we are given with the graph and we have to find what will be the maximum profit or…

Q: A Norman window is a rectangle with a semicircle on top. Suppose that the perimeter of a particular…

A: Let, x denotes the half width of the rectangle.y denotes the height of the rectangle.And…

Q: Find the maximum profit and the number of units that must be produced and sold in order to achieve…

A: Given  R(x)=x2+110x+60C(x)=1.1x2+10x+80

Q: A farmer is going to divide her 30-acre farm between two crops. The seed for crop A costs $25 per…

A: Given :- total farm area available = 30 acre. Cost of seed per acre in crop A = $25 Cost of seed per…

Q: Furnco manufactures desks and chairs. Each desk uses 4 units of wood, and each chair uses 3. A chair…

A: assuming that x unit of desks and y unit of chairs are produced by company. Since profit is to be…

Q: The Penn State Math Club has determined that in order to successfully tutor x Math 110 students in…

A: