Find the optimum level of output and profit from the cost function TC = 50 + 6Q2 and price P = 100 – 4Q Also derive marginal cost and marginal revenue
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Find the optimum level of output and profit from the cost function
TC = 50 + 6Q2
and price
P = 100 – 4Q
Also derive marginal cost and marginal revenue
Step by step
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- The total revenue curve of a firm is R(q) = 40q − 12q^2 and its average cost A(q) =1/30q^2− 12.85q + 20 + 400/q ,where q is the firms output. (I) Determine the level of output for which the firm's profit is maximized. (ii) What is the firm's maximum profit?A firm has the following revenue and cost functions. TR = 90 Q – Q2 TC = 2Q 2+ 30 Q Determine the quantity level at which the firm maximizes its total profit. (Hint: use marginal revenue = marginal cost rule)The demand and total profit function, P(x) for rooms in a hotel are given as follows. 3x = 600 - P P(x) = 450x – 3.5x2 - 4000 Where p is the price in ringgit per room and x is the quantity of room rented. Determine the marginal cost when 2 rooms are rented
- Suppose that the unit price of a commodity of firm X is defined by: P- 90 - Q and the total cost of producing this commodity is defined by the cost function: TC- 100+0.5Q, compute i. Total Revenue (TR) ii. Marginal Revenue(MR) and interpret the result ii. Marginal cost (MC) and interprets the result iv. Find the level of output and price which maximize profit. v.Find the maximum profit vi. Check the second order conditionA company is the sole producer of holographic TVs. The daily demand for these TVs is Q=10,200 - 100P, where Q is the quantity demanded and P is the price. The cost of producing the TVs is (note that this implies that marginal cost is equal to Q, MC = Q). What is the company’s total revenue schedule? What is the company’s marginal revenue schedule? What is the profit maximising number of TVs that the company must produce each day? What price should it charge per TV? What is the daily profit?A firm has the following revenue and cost functions. TR = 60 Q – Q^2TC = 1/2 Q^2 +30Q + 30Determine the quantity level at which the firm maximizes its total profit.(Hint: use marginal revenue = marginal cost rule)
- The total revenue curve of a firm is R (q) = 40q - 12q2 and its average cost A(q) = 1/30q2 - 12.85q +20 + 400/q, where q is the firm's output (1) Determine the level of output for which the firm's profit is maximizedIf the marginal revenue is MR=26-Q , find the highest level of production (Q) of the firmwhen its total revenue is 70 dollar.If a firm is a price taker, then its marginal revenue will always equal * a)price. b)zero. c)total cost. d)one.
- Suppose the marginal cost and marginal revenue (in ¢000) for a product produced by a company is estimated to beMC=q+35 MR=560+22q−q2Where q is the quantity produced and the firm’s break-even is 5 units per weekYou are Required to1. determine the total cost and the total revenue function in terms of q.2. estimate the output at which profit is maximize3. calculate the maximum profitSuppose the revenue function y=R(x) is linear, and points (x,y) of (10,550) and (13,715) are on the line. a. What is the marginal revenue? b. Suppose also the total costs are given by C(X) = 150 + 15x +2x^2. Find the x-value that maximizes profit.A firm has the following revenue and cost functions.TR = 60 Q – Q2TC =12Q2 +30 Q + 30Determine the quantity level at which the firm maximizes its total profit
