excel

5. TriCity Styrofoam Manufacturing TriCity Manufacturing (TCM) makes Styrofoam cups, plates and sandwich and meal containers. Next week's schedule calls for 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 MI can process Styrofoam sheets with a maximum width of 12 inches. The width capacity of machine M2 is 16 inches and the width capacity of machine M3 is 20 inches. The small sandwich containers require 10-inch Styrofoam sheets. Thus, these containers can be produced on each of these three machines. The large sandwich containers require 12-inch Styrofoam sheets. Thus, these containers can also be produced on each of these three machines. However, the meal containers require 16-inch Styrofoam sheets. Thus, meal containers cannot be produced on MI. The waste produced depends on the machine used as reported in Table 1. I incurred in the production of all 3 containers because Styrofoam is lost in the heating and forming process as well as final trimming of the product. The amount of waste generated varies depending upon the container and the machine used. The table shows the waste in square inches for each machine product combination Machine Small sandwich Large Sandwich Meal MI 20 15 NA M2 M3 24 32 28 18 35 36 Table: Waste for each machine and product combination Production rates also depend upon the container produced and the machine used. The following Table 2 shows the production rates in units per minute for each combination of machine and product. For example, 20 small sandwich containers can be produced per minute on M1. The rate for M2 is 24 per minute and for M3 32 small sandwich containers per minute. Total time available on each machine 35 hours M1, 35 hours M2, and 40 hours M3 Machine Small sandwich Large Sandwich Meal 26 minute 43/minute 41/minute 30/minute 57 minute Table: Rate per minute production for each machine and product combination Costs associated with reprocessing waste are going up. TriCity wishes to minimize waste. 29 minute MI M2 M3 53./minute 44 minute Costs associated with reprocessing waste are going up. TriCity wishes to minimize waste. a. Determine the optimal production plan. This requires determining how many of each type of container should be manufactured on each machine. b. In your formulation there are 8 decision variables. Why are there not 9 decision variables? c. Which machines are not working to capacity? How much available time is there for each machine not at capacity/ d. Of all the product and machine combinations, which one in the optimal solution is sensitive to small changes in the amount of waste? e. How much would the waste have to decrease for an unused product machine combination to be included in the optimal production plan. f. Make a change in the waste such that this combination is included in the optimal solution? Describe the difference between the optimal solution in part a and part e