Minimize the cost of operating 3 different types of machines while meeting product demand over a week's time. Each machine has a different cost and capacity. There are a certain number of machines available for each type. Information on machines Initial cost per day Additional cost per product Products per day (Max) Number of machines Alpha-1000 \$200 \$1.00 40 8 Alpha-2000 \$275 \$1.80 60 5 Alpha-3000 \$325 \$1.90 85 3 Number of machines to use Monday Tuesday Wednesday Thursday Friday Alpha-1000 0 0 0 0 0 Alpha-2000 0 0 0 0 0 Alpha-3000 0 0 0 0 0 Number of products to make per day Monday Tuesday Wednesday Thursday Friday Alpha-1000 0 0 0 0 0 Alpha-2000 0 0 0 0 0 Alpha-3000 0 0 0 0 0 Made 0 0 0 0 0 Carry-over 0 -600 -1400 -2400 -3125 Total 0 -600 -1400 -2400 -3125 Demand 600 800 1000 725 750 Maximum number of products that can be made Monday Tuesday Wednesday Thursday Friday Alpha-1000 0 0 0 0 0 Alpha-2000 0 0 0 0 0 Alpha-3000 0 0 0 0 0 Total Cost \$0.00 \$0.00 \$0.00 \$0.00 \$0.00 \$0.00 Problem A company has three different types of machines that all make the same product. Each machine has a different capacity, start-up cost and cost per product. How should the company produce its product with the available machines to meet the demand over a week's time? Solution The solution is very similar in structure to the one found on worksheet Alloc1. 1) The variables are the number of machines to use and the number of products to make on each machine. In worksheet Alloc2, these given the names Products_made and Machines_used. 2) First, there are the logical constraints. These are Products_made >= 0 via the Assume Non-Negative option Machines_used >= 0 via the Assume Non-Negative option Machines_used = integer. Second, there are the demand and capacity constraints. These are: Alpha1000s_used <= Alpha1000s_available Alpha2000s_used <= Alpha2000s_available Alpha3000s_used <= Alpha3000s_available Products_made <= Maximum_products Total_made >= Demand 3) The objective is to minimize cost. This is defined on the worksheet as Total_cost.. Remarks Please see the comments on integer constraints in worksheet Alloc1. In this model we allow for products made on one day to be carried over to the next. This makes it possible to meet a demand for one day that exceeds the capacity of the machines on that particular day.