Question

# Linear Programming A company makes two products with a profit of one dollar per ton of...

Linear Programming

A company makes two products with a profit of one dollar per ton of product A and two dollars per ton of product B. To produce one ton of product A two tons of water is needed and for one ton of product B one ton of water is needed. The factory only has 20 tons available to produce the products.

The product needs a process of two steps.
For the first step the company hires a person which must work for at least 36 weeks. One ton of product A requires 10 weeks of work on step one and one ton of product B requires one week of work on step one.
Step two another person is hired who also must work for at least 36 weeks. On step two, one ton of product A requires two weeks of work and one ton of product B requires 6 weeks of work.

1. Formulate the problem - Draw the feasible region (polygon) (maybe excel)
2. Find the optimal solution. Report the maximum profit and how many ton of product
A and B should be produced to achieve the optimal profit.
3. Which constraints are not binding for the optimal solution (has a slack) ?
4. Get the sensitivity report and explain what it tells you.