3. a. A firm produces two different kinds A and B of a commodity. The daily cost of producing a units of A and y units of B is C(x, y) = 0.04x² +0.01xy +0.01y² + 4x +2y + 500 A sells for $15 per unit and B sells for $9 per unit. Find the daily production levels of x and y that maximize profit per day b.A firm's production function is given by F(K,L) = KL. Each unit of K costs $1.2 and each unit of L costs $0.6. Each unit of output sells at $12. Find the optimal level of K and L that maximize profit.

A manufacturing process has a total cost function given by the equation C = 10 + 4x and a total revenue function given by the equation R = 22x - 4x2 where x is the quantity produced in ’00 units and C and R , are both N$’00. i. Using the cost equation, C = 10 + 4x, identify the value of the company’s fixedcosts (i.e. those that remain constant irrespective of the quantity produced) andvariable costs (i.e. those that vary according to production) for thismanufacturing process. ii. Construct a table to calculate the value of C and R using the values 0, 1, 2, 3, 4and 5 for x. iii. (Using the data from the table in (ii), plot a fully labelled graph for C and Ragainst x. Use the graph drawn in (iii) to determine:iv. The quantity of units produced where the manufacturing process breaks even(i.e. where neither a profit nor a loss is made). v. The range of x in which the manufacturing process makes a profit and the rangein which the manufacturing process makes a loss. vi. The profit or loss…

11. A clothing company sells two types of shoes A and B. The price function for shoe A is (p = 80 5x) dollars. The price function for shoe B is (q = 100 6y) dollars, where (x) and (y) are the numbers of shoe A and shoe B sold per day. The company's cost of producing each shoe A is $20/shoe and the cost of producing each shoe B is $16/shoe. The fixed costs are $200/day. a. Find the Revenue function from selling these two types of shoes. b. Find the Cost function. c. Find the Profit function. d. Perform D-Test. e. Find how many shoes and at the prices at which they should be sold to maximize the daily profit. f. Find the maximum daily profit. 17

Answer all parts. Suppose that a monopolist offers two different products with demand functions P1 = 56 – 4q, Р2 3D 48 — 2q2 The monopolist's joint cost function is C(41, 92) = qỉ + 5q192 + q3 %3D a. Write out the monopolist's profit function as a function of b. Differentiate the profit function with respect to q, and q2.Explain intuitively why we take the derivative of the function. c. Solve the first order conditions using Cramer's rule. d. Use the values that you found in part c to find the prices in each market and the profit that is made by the monopolist. e. Use the second order condition for a maximum to check whether or not the and 92. values that you have computed do represent a maximum.