A manufacturer wants to invest $100000 in the production of two products A and B. The cost and demand functions for the two products are: C(q) = 509 +30000 C(q) = 100q +20000 P.(9) = 1500-4 P,(9)=1000-4 Letx denote the number of units of product A, and let y denote the number of units of product B. ii) How many units of each product should be produced in order to maximize the profit?

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A manufacturer wants to invest $100000 in the production of two products A and B. The cost and demand functions for the two products are: C(q) = 509 +30000 C(q) = 100q +20000 P.(9) = 1500-4 P,(9)=1000-4 Letx denote the number of units of product A, and let y denote the number of units of product B. iii) What will the maximum profit be?

A company produces 3 products, A, B, and C, that require processing by three machines, I, II and III. The time in hours that is required for processing one unit of each product by the three machines is given by the following table: ABC 312 II 1 2 1 111 2 4 1 Machine I is available for 440 hours, machine II for 310 hours and machine III for 560 hours. Find how many units of each product should be produced to make use of ALL available time on the machines. Letx, y, and z represent the number of product A, B, and C produced.

4. In all of this question let q> 0 represent quantity (i.e. number of units) of some product and 2250 let p > 0 represent unit price in $ per unit). Assume a demand function p= 400 – 50q+ __800 In(q +5) and an average cost function i= (a) State the profit function. [4 points] (b) Find the quantity that maximizes profit and calculate the maximum profit. Sufficiently justify your answer. (11 points)

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