TriCity Manufacturing (TCM) makes Styrofoam cups, plates, and sandwich and meal containers. Next weeks schedule calls for

TriCity Manufacturing (TCM) 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 containers, and 65,000 meal containers. To make these containers, Styrofoam sheets are melted and formed into final products using three machines: M1, M2, and M3. Machine M1 can process Styrofoam sheets with a maximum width of 12 inches. The width capacity of machineM2is 16 inches, and the width capacity of machineM3is 20 inches. The small sandwich containers require 10-inch-wide Styrofoam sheets; thus, these containers can be produced on each of the three machines. The large sandwich containers require 12-inch-wide sheets; thus, these containers can also be produced on each of the three 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 three containers because 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 square 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 table 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,
TCM 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 formulated in part (a) to determine the production schedule. How much waste is generated? Which machines, if any, have idlecapacity?

Transcribed Image Text:

Small Sandwich 20 24 32 Large Sandwich 15 28 35 Meal Machine MI M2 M3 18 36 Small Sandwich 30 45 60 Large Sandwich Meal Machine Mi M3 52