PRICE-DEMAND AND COST FUNCTIONS FOR PRODUCING AND SELLING 'X' FOODS ARE GIVEN BY P(X) = 70-0.25X AND C(X)=0.5X²+10X+800, RESPECTIVELY, WHERE P AND C ARE IN PESOS. 1. FIND THE MARGINAL PROFIT WHEN 20 FOODS ARE SOLD. 2. AT WHAT PRODUCTION LEVEL IS THE AVERAGE COST PER FOOD AT A MINIMUM?
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- A firm produces two different kinds, A and B, of a commodity. The daily cost of producingx units of A and y units of B isC(x, y) = 2x2 − 4xy + 4y2 − 40x − 20y + 514Suppose that the firm sells all its output at a price per unit of $24 for A and $12 for B. Findthe daily production levels x and y that maximize profit. (Be sure to show your first andsecond order conditions.)Marginal revenue of a product is the incremental revenue of selling an additionalunit of that product. Let, the revenue of selling 20 units of a product beRs. 15,000 and the revenue of selling 21 units of the same product beRs. 15,085. Then, the marginal revenue of selling the 21st unit____?. Marginal Cost Suppose the monthly total costfor the manufacture of 19-inch television sets isC(x)= 2546 + 98x, where x is the number of TVsproduced each month.a. What is the slope of the graph of the total costfunction?b. What is the marginal cost for the product?c. Interpret the marginal cost for this product
- Let a firm’s production function be f(K,L) = min{2K,L}.a) Solve for the contingent demand functions for Kand L.b) Substitute the contingent demand functions in the total cost that you minimized in parta) to obtain the total cost function.c) Find the minimal amount of Kand Lnecessary to produce Q= 8 when v= 2 andw= 1 (with minimal possible cost).d) Suppose the price wincreases from 1 to 2. What happens to the demands for KandLand the total cost?A firm face the production function:Q=120L+200K-L2-2K2It can buy L at N5 a unit and K at N8 a unit with a budget of N70. Use any method ofyour choice to find the maximum output the firm can produce.A firm has the production function F(L, K) = L^1/2 + K^1/2The price of labor is $10 and the price of capital is $15. The firm has a production goal of Q = 100 units ofoutput.a) Neatly specify this firm’s cost minimization problem, using the particulars associated with this problem.b) Give two equations that an interior solution satisfies, tailoring your equations to the particulars of thisproblem.c) Solve the two equations for the firm’s optimal choice. Show your work.
- omly typed answer he cost of ingredients for a turkey sandwich at The Pit Room is $5, and the daily demand function for this sandwich is d(p) =1200 - 100p. What price should the seller charge to maximize its daily total contribution? Round your final answer to two decimal places.Revenue and Cost The total revenue function for LED TVs is given by R = 1050x dollars, and the total cost function for the TVs isC = 10,000 + 30x + x2dollars, where x is thenumber of TVs that are produced and sold.a. Which function is quadratic, and which is linear? b. Form the profit function for the TVs from thesetwo functions.c. Is the profit function a linear function, a quadraticfunction, or neither of these?The cost, in dollars, of producing x yards of a certain fabric is C(x) = 1100 + 13x − 0.1x2 + 0.0005x3. (a) Find the marginal cost function. C'(x) = (b) Find C'(500) and explain its meaning. What does it predict? C'(500) = and this is the rate at which costs are increasing with respect to the production level when x = . C'(500) predicts the cost of producing the ---Select--- 499th 501st 401st 599th 500th yard. (c) Compare C'(500) with the cost of manufacturing the 501st yard of fabric. (Round your answers to four decimal places.) The cost of manufacturing the 501st yard of fabric is C(501) − C(500) = − 45,100 ≈ , which is approximately C'(500).
- Minimization CT = W1X1 + W2X2 Hold it: Y = X11/3 X21/6 where X1 and X2 are the productive factors and W1 and W2 are their prices, respectively. Determine: If X2 = 27 and W2 = 2 a) The short-run cost functionAverage and marginal profit Let C(x) represent the cost ofproducing x items and p(x) be the sale price per item if x items aresold. The profit P(x) of selling x items is P(x) = xp(x) - C(x)(revenue minus costs). The average profit per item when x items aresold is P(x)/x and the marginal profit is dP/dx. The marginal profitapproximates the profit obtained by selling one more item, given that x items have already been sold. Consider the following cost functions Cand price functions p.a. Find the profit function P.b. Find the average profit function and the marginal profit function.c. Find the average profit and the marginal profit if x = a units are sold.d. Interpret the meaning of the values obtained in part (c). C(x) = -0.02x2 + 50x + 100, p(x) = 100 - 0.1x, a = 500A firm has a linear demand function for its product. When the price of the product isSh.220, the quantity demanded is 40 units. When the price increases to Sh.240, thequantity demanded becomes 30 units. In addition, the firm’s marginal cost function isgiven by:MC = 40q – 2q2 + 2Fixed cost = Sh.5 millionWhere q = quantity demanded, MC = marginal cost (Sh. million)Evaluate the level of output that maximizes profits.