A small company produces two types of margarine: type A (Lowfat) and type B (Verylowfat). The production costs are €0.7 per kg for type A and €0.8 per kg for type B: The daily demands 94 of type A and qe of type B are given by 4A = 160-200PA+100PB and qB = 60+100PA - 100qB where PÅ and PB represent the prices (in € per kg) for the two types of margarine. It is known that the daily demand of type B is 25 kg. a. Determine the profit function P that gives the total profit for the two types of margarine in terms of PA b. What selling prices give the maximum profit? Use derivatives to solve this question. c. Determine the maximum profit.

Assume that the production of 1 unit of magnesium requires 0.8 units of magnesium and 0.2 units of aluminum, and that the production of 1 unit of aluminum requires 0.3 units of magnesium and 0.2 units of aluminum.

With fixed costs of Ksh. 400,000, a firm has average total costs of Ksh. 3,000 and average variable costs of Ksh. 2,500. Its output is?

Huntco produces tomato sauce at five different plants. The tomato sauce is stored at one of three warehouses (W/H). The per-ton cost (in hundreds of dollars) of producing tomato sauce at each plant and shipping it to each warehouse; capacity of the plants; and the fixed cost of setting up the plants are given in the below table. Cost to ($/ton) DIIT From plant WH 1 WH2 WH 3 Capacity (tons) Fixed cost (x1,000 in $) Plant 1 8 10 12 300 Plant 2 200 45 Plant 3 6 300 Plant 4 5 7 200 42 Plant 5 7 6 400 40 Huntco has 4 customers. The cost of shipping a ton of sauce from each warehouse to each customer; customers' demand quantities; and the fixed cost of maintaining the warehouses are given below. Cost to ($/ton) Fixed cost From WH Customer 1 Customer 2 Customer 3 Customer 4 (x1,000 in $) WH 1 40 80 90 50 30 WIH 2 70 70 60 80 40 WIH 3 80 30 50 60 30 Demand (tons) 200 300 150 250 We would like to meet the demand at minimum cost using an appropriate mathematical model. • Decision variables? •…