Question

1. Shiny Chemical Company produces specialty products for the automobile industry. Shiny produces a cleaner (Cln) and a polisher (Pol). Realized profit is $10 per cleaner and $30 per polisher. Both products require processing through the same machines, machine one (m1) and machine two (m2), but Cln requires 4 hours in m1 and 8 hours in m2, whereas Pol requires 6 hours in m1 and 4 hours in m2. During the upcoming month m1 has 12 hours available capacity and m2 has 16 hours available capacity. How much of each product should be produced to reach an optimal profit?
   1. Assistance:

Objective function:     max π = 10Cln +30Pol

Subject to:                   4Cln + 6Pol ≤ 12         for machine 1

                                    8Cln + 4Pol ≤ 16         for machine 2

                                    Cln ≥ 0

                                    Pol ≥ 0

Answer 1

To maximize the profit we have to decide what amount of each product should be produced.

This problem can be solved using linear programming techniques.

First we will solve these two simple linear inequalities.

After solving these two two linear equations, we will get some point of intersection i.e (2/3,1).

When we plot these two lines on graph we consider the region under which we will maximize the profit.

Considering this reason, we get 4 different points and they arr (2,0), (2/3,1), (0,2), (0,0).

We can simply come to the conclusion after substituting these points in our objective equation i.e 10*cln+30*pol.

We will have maximum profit if shiny company produces 2 polishers and no cleaners from machine 2.