Tri City Manufacturing makes Styrofoam cups plates and sandw

Tri City Manufacturing makes Styrofoam cups, plates and sandwich and meal containers. Next week\'s schedule calls for the production of 80,000 small sandwich containers, 80,000 large sandwich containters, and 65,000 meal containers. To make these containers, Styrofoam sheets are are melted iand formed into final products using three machines. M1, M2, and M3. Machine M1 can process Styrofoam sheets with a max width of 12 inches, M2 with max width of 16 inches and M3 with max width of 20 inches.

The small sandwich containers require 10 inch wide Styrofoam sheets, thus these containers can be produced on each of the 3 machines.

However, the meal containers require 16 inch wide Styrofoam sheets, so the meal containers cannot be produced on Machine M1.

Waste is incurred in the production of all 3 containers since Styrofoam is lost in the heating and forming process as well as in the final trimming of the product. The amount of waste generated varies depending upon the container produced and the machine used. The following table shows the waste in squre inches for each machine and product combination. The waste material is recycled for future use.

Production rates also depend upon the container produced and the machine used. The following tabe shows the production rates in units per minute for each machine and product combination. Machine capacities are limited for the next week. Time available is 35 hours for Machine M1, 35 hours for Machine M2, and 40 hours for Machine M3.

a. Costs associated with reprocessing the waste material have been increasing. Thus, the company would like to minimize the amount of waste generated in meeting next week\'s production schedule. Formulate a linear programming model that can be used to determine the best production schedule.

b. Solve the linear program fromulated in part a. to determine the production schedule. How much waste is generated? Which machines, if any, have idle capacity?

*Please provide detailed calculations and explaination for all steps!

Solution