Question: A caterer has undertaken a contract for a series of dinners to be given on each of 4 successive days. Suppose there would be 100 dinners in day 1, 200 dinners in day 2, 300 dinners in day 3 and 400 dinners in day 4. The caterer must purchase napkins especially for these dinners. Each new napkin costs £1. Two types of napkin laundry service are available to the caterer: regular service takes 3 days and costs 30p per napkin; express service takes 2 days and costs 50p per napkin. After the series of dinners the napkins are thrown away. The manager wishes to minimize the total cost of distributing the napkins used in each day, including the new ones and the laundered ones.
- Formulate the caterer's napkin problem as a linear programming problem. Take care to define all the terms you use.
- Find the optimal solution problem in (i) using the simplex method Take care to provide the Simplex tableau and iteration steps.