3. Consider Q(L, K) = 10L0.5 K0.4. Suppose that the unit output price is $5, and the unit labor cost and unit capital cost are $12 and $40, respectively. The firm's profit function is then g(L,K) = 5Q (L, K) - 12L-40K. Find the maximum profit.
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- 1. It costs $25,000 to build 30 refrigerators. It costs $30,000 to build 40 refrigerators. Assuming that the cost function is linear, find the cost function C(x) where x is the number of refrigerators built. If each refrigerator sells for $1500, find the revenue function, profit function, and break-even point.= Suppose that the marginal revenue for firefighting protective clothes is MR marginal cost is MC = 3.5x + 15 with a fixed cost of $295. Assume R(0) = 0. a) How many units will result in a maximum profit? x = b) Find the revenue function. R(x) c) Find the cost function. C(x) 337.5 4x and the d) What is the maximum profit (to the nearest dollar)? The maximum profit isSuppose that the a firm's cost function is given by: C(q)=1+3q2. Then, the expression for this firm's profit function is? A) Profit(a)=pq-6q. B) Profit(a)=pg-1-q?. C) Profit(a)=pq-1-3q?. D) Profit(a)=pg-1-6q. E) Profit(a)=pg-3q?.
- The manufacturer of an energy drink spends $1.28 to make each drink and sells them for $3.27. The manufacturer also has fixed costs each month of $835.8.ⓐ Find the cost function C when x energy drinks are manufactured. C(x)= ⓑ Find the revenue function R when x drinks are sold. R(x)= ⓒ Find the break-even point. (Enter you answer as an ordered pair of the form (x,$). __________________Suppose the Sunglasses Hut Company has a profit function given by P(q) - 0.01q² + 5q - 40, = where q is the number of thousands of pairs of sunglasses sold and produced, and P(q) is the total profit, in thousands of dollars, from selling and producing a pairs of sunglasses. A) Find a simplified expression for the marginal profit function. (Be sure to use the proper variable in your answer.) Answer: MP(q) = B) How many pairs of sunglasses (in thousands) should be sold to maximize profits? (If necessary, round your answer to three decimal places.) Answer: thousand pairs of sunglasses need to be sold. C) What are the actual maximum profits (in thousands) that can be expected? (If necessary, round your answer to three decimal places.) Answer: thousand dollars of maximum profits can be expected.A company produces very unusual CD's for which the variable cost is $ 15 per CD and the fixed costs are $ 50000. They will sell the CD's for $ 79 each. Let a be the number of CD's produced. Write the total cost C as a function of the number of CD's produced. C =$ Write the total revenue R as a function of the number of CD's produced. R=$ Write the total profit P as a function of the number of CD's produced. P=$ Find the number of CD's which must be produced to break even. The number of CD's which must be produced to break even is Question Help: Video Submit Question
- 8. Consider the following cost function: C(Q) = 20Q3 – 15Q? + 10Q. Answer the following questions: What is the range of output where this firm has economies (a) of scale. (b) cost function. You must compute the expression using the cost function given in this question. What is the measure of cost-output elasticity (Ec) for thisThe company AffordableStuff sells cell phones. The marginal cost for each cell phone is given by the equation C(x) = 0.01x² – 3x + 229. a is the number of cell phones manufactured and sold. The marginal revenue function is R(x) = 429 – 2.x. Both C(x) and R(x) are given in dollars. a) Where do these curves intersect? What do those intersection points mean? b) Find the area between the curves, using end points that make sense. Round to the nearest cent. c) What does the area under the curve mean in this case?-n 5. A company estimates that the total revenue, R, in dollars, received from the sale of q items is R(q) = 3000+ln(2000+q²) and the marginal cost is MC(q) = 0.05q² +1.6q – 50. Calculate and interpret the marginal profit at q = = 10.
- The hourly operating cost of a plane which seats up to 405 passengers is estimated to be $5,328. If an airline charges each passenger a fare of $120 per hour of flight, find the hourly profit P it earns operating the plane as a function of the number of passengers x. [HINT: The cost function is constant (variable cost = 0).] P(x) = Specify the domain. (Enter your answer using interval notation.) What is the least number of passengers the plane must carry to make a profit? (Round your answer up to the nearest whole number.) passengersSuppose the firm achieves total revenue of $1,000 by selling 150 units while facing total costs of $900. If the firm produces and sells 151 units, its total revenue is $1,005, and its total costs are $950. Should the firm produce and sell the extra unit? Group of answer choices yes, since marginal profit is positive yes, since profits are positive no, since marginal profit is negative no, since marginal profit is positive You have recently learned that the company where you work is being sold for $1,000,000. The company's income statement indicates next year's profits of $30,000, which have yet to be paid out as dividends. Assuming the company will remain a "going concern" indefinitely and the interest rate will remain constant at 7%, at what (constant) rate does the owner believe that profits will grow? (Hint: the price the owner was willing to pay is the present value of the firm's future cash flows) Group of answer choices 6% 5% 4% 4.5%Sergio Lopez is a publisher of Latin American poetry. His fixed cost is $525, and the cost to produce each individual copy of his book is $3.50. Currently, Sergio is selling these books for $6 each. So far this year, he has produced x a. Write a linear cost function C for Sergio’s book production, in terms of x. b. Find the linear revenue function R for selling x copies of the book. Remember that P(x) = (price)x. c. Use and 1b. to determine the profit function P for selling x books. Write the formula in simplified form. d.Use your answer for 1c to determine the profit, in dollars, for selling 300 books.
