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- = 40q – 12q² and its where q is the firm's output. (b) The total revenue curve of a firm is R(q) 400 average cost A(q) q² – 12.85q + 20 + i. Derive an expression C(q) for the firm's total cost function. ii. Derive an expression II(q) for the firm's profit function. iii. Is the rate of change of profit increasing or decreasing when the ouput level of the firm is 10 units? iv. Determine the level of output for which the firm's profit is maximized. v. What is the firms's maximum profit?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.Question 1 A computer retailing company specializes in the sale of jump drives to community college students The demand function for jump drives is p=2x- +10=1000 dollars For the samne company the average cost function is given as. 2+36v-1600 - dollars Where pis the price n dollars and x represents units ofiourput. Determine the revenue function Determine the cost funetion Determine the profit function Find the price and output that will maximıze profir, Find the maximum profit 11 111) Iv) Ouestio n 2
- and The price-demand and cost functions for the production of microwaves are given as p=200- X 30 C(x) = 52000 + 110x, where x is the number of microwaves that can be sold at a price of p dollars per unit and C(x) is the total cost (in dollars) of producing x units. (D) Evaluate the marginal revenue function at x = 1500. R'(1500) (E) Find the profit function in terms of x. P(x) = (F) Evaluate the marginal profit function at x = 1500. P'(1500)=ONE A. Suppose the marginal cost and marginal revenue (in ¢000) for a product produced by a company is estimated to be �ж=�35 �х=560+22�Ȓ� Where �is the quantity produced and the firm’s break-even is 5 units per week You are Required to I. determine the total cost and the total revenue function in terms of q.The demand curve of a firm is p=1200– 21q and its total cost is C(q) = 2q – 66q² +600q+1000 where q is the output of the firm (in thousands). (i) Derive an expression R(q) for the firm' s revenue function. (ii) Derive an expression II(q) for the firm' s profit function. (iii) Is the rate of change of profit increasing or decreasing when the output level of the firm is 10,000 units?
- Marginal Revenue for an Apartment Complex Lynbrook West, an apartment complex, has 100 two-bedroom units. The monthly profit (in dollars) realized from renting x apartments is represented by the following function. P(x) = -6x² + 1620x - 36000 (a) What is the actual profit realized from renting the 61st unit, assuming that 60 units have already been rented? $ 40,434 X (b) Compute the marginal profit when x = 60 and compare your results with that obtained in part (a). $ 900A donut shp has a fixed cost of $92000 per day and a varibale cost of $2 for each donut produced. If the donuts are sold to distributors for $5 each. What is the price-demand function? What is the revenue function?he total revenue curve of a firm is R(q)=40q−12q and its average cost A(q)=130q−12.85q+20 +400q,where q is the firms output. i. Derive an expression C(q) for the firms total cost function. ii. Derive an expression Π(q) for the firms profit function. iii. Is the rate of change of profit increasing or decreasing when the ouput level of the firm is 10 units? iv. Determine the level of output for which the firms profit is maximized. v. What is the firmss maximum profit?
- 2) The owner of a restaurant that you are thinking of purchasing, tells you for x customers per week the weekly cost and revenue in dollars is C(x) = 15000+2x and R(x) = 500x-3x² a) Find the profit function P(x) b) Find the break-even quantities rounding properly to a whole number. (Hint: Use the Quadratic formula) c) Why is the minimum break-even quantity important?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 firm’s output. (i) Derive an expression C(q) for the firm’s total cost function. (ii) Derive an expression for the firm’s profit function. (iii) Is the rate of change of profit increasing or decreasing when the output level of the firm is 10 units? (iv) Determine the level of output for which the firm's profit is maximized (v) What is the firm’s maximum profit?A company manufacturing laundry sinks has fixed costs of $100 per day but has total costs of $2,500 per day when producing 15 sinks. The company has a daily demand function of q = 360 − p, where q is the number if laundry sinks demanded and p is te price of a laundry sink. (e) What is the maximum profit?