Linear Programming

For EACH LP exercise: It is essential that you show all work: equations, tables, systems, and that the graph explains all the important variables. In other words, the scale of the graph should be selected properly, and all the constraints, the feasible area, the critical (comer) points should be SOLVED ALGEBRA/CALLY (systems) and indicated dearly. The line(s) also have to be labeled (colored) clearly. Points will be taken offfor sloppiness. Use DESMOS or USE GRAPH PAPER AND COLORS! Answer the question with a complete sentence in context - explaining the meaning of the solution. 1. A company manufactures two types of cleaners. One is an all-purpose cleaner (AP) and the other is an industrial strength cleaner (IS). Each cleaner is a mixture of three chemicals, as shown below. The profit per kiloliter from the AP cleaner is $20 and the profit per kiloliter from the IP cleaner is $30. The inventory of the company shows 480 liters of surfactants, 180 liters of enzymes, and 720 liters of solvents available. Assuming the company can sell all the cleaner it produces, find the number of kiloliters of each cleanser the company should produce to maximize profit. What is the maximum profit? 2. A manufacturer wants to maximize the profit of two products. Apples yields a profit of $2.50 per unit, and Pears yields a profit of $4.00 per unit. Market tests and available resources have indicated the following constraints: - The combined production level should not exceed 1200 units per month. - The demand for pears is no more than half the demand for apples. - The production level of apples is less than or equal to 600 units plus three times the production level of pears