First West Chemical Company produces two chemical ingredients for pharmaceutical firms; formula X and formula Y. Production of each ingredient requires two processes. A unit of Formula X requires 4 hours in process 1 and 3 hours in process 2. A unit in formula Y requires 2 hours in process 1 and 5 hours in process 2. The normal operating production times for the two processes are as follows: process 1, 70 hours and process 2, 60 hours. The production process of formula X results in one unit of a by-product called XZ. Four (4) units of X produce 1 unit of XZ. The production process for formula Y yields 5 units of a by-product, YK for each unit of formula Y. The unit profits for formulas X and Y are $10,000 and $15,000 respectively. By products XZ yields $6000 unit profit. By product YK yields a $3000 unit profit for up to 15 units. Because of the limited market and the danger involved in handling the material, any by product YK in excess of 15 units must be destroyed at a unit cost of $4,000. Also due to storage regulations, no more than 15 units of Formula X can be produced.

The management at this chemical company has established the following goals in order of importance:

1) Avoid any underutilization of normal operation hours of each of the two processes. Each of equal importance.

2) Meet the outstanding orders for 8 units of formula X and 7 units of Formula Y. Each of equal importance.

3) Limit any overtime operation of each of the two production process to 10 hours. Each of equal importance.

4) Achieve a profit goal of $220,000

5) Limit the production of by-product YK to 15 units.

6) Minimize the overtime operation of the production processes. Each of equal importance.