What is the maximum profit a firm can make if it faces the demand schedule p = 660 − 3q and the total cost schedule TC = 25 + 240q − 72q2 + 6q3? 2. If a firm faces the demand schedule p = 53.5 − 0.7q, what price will maximize profits if its total cost schedule is TC = 400 + 35q − 6q2 + 0.1q3? 3. Find the extreme value(s) of each of the following four functions, and determine whether they are maxima or minima: a) Z=X2+xy+2y2+3 b) Z=-x2-y2+6x+2y 4. Using your knowledge of economics to apply appropriate restrictions on their domain, say whether or not the following functions have maximum or minimum points. a) TC = 12 + 62q − 10q2 + 1.2q3 b) TC = 6 + 2.5q c) p = 285 − 0.4q

The demand function of a good is given byP = 140 − 35Qwhere P denotes the price and Q the quantity.(a) Write down the revenue R as a function of the quantity Q.(b) Find the quantity Q that maximizes the revenue and find the maximumrevenue

A monopolistic manufacturer produces two different brands of a product whose demand functions are P1 = 56 - 4Q1P2 = 48 - 2Q2and the joint cost function is TC = Find the profit maximising level of output and the price that would be charged for each brand. Also find the maximum profit.

Answer the next question based on the demand and cost schedules for a monopolistically competitive firm given in the table below. Price Quantity Demanded Total Cost Output$20 1 $10 118 2 20 216 3 29 314 4 36 412 5 40 510 6 42 6 What output quantity will the monopolistically competitive firm produce to maximize profits?

A firm’s total revenue function and total cost function are as follows:TR = 200Q – Q2TC = 50 + 20Q +0.5Q2Use this information the answer the following three questions (Q16-Q18).To maximize total revenue, how much quantity should the firm produce?a.Q = 200b.Q = 100c.Q = 150d.Q = 50To minimize average cost, how much quantity should the firm produce?a.Q = 20b.Q = 10c.Q = 100d.Q = 200To maximize profit, how much quantity should the firm produce? a.Q = 40b.Q = 80c.Q = 60d.Q = 20

A monopolist has a demand function p=152,5−3q, and costs given by TVC=0,5q3−15q2+175q and TFC=0. Find the loss profits points. a. 0<q<2 and q>22 b. 2<q<22 and q>0 c. q>0 and q<2 d. q<22