A cake mix manufacturer has 4 different plants that all require a certain amount of sugar. There are 5 different companies where the sugar can be bought. Where should the company buy the sugar and how much should it buy, to minimize cost of sugar and shipping? Company 1 Company 2 Company 3 Company 4 Company 5 Sugar prices (per ton) \$40 \$49 \$47 \$45 \$44 Cost of shipping from companies to plants (per ton) Company 1 Company 2 Company 3 Company 4 Company 5 Plant 1 \$8 \$4 \$5 \$4 \$3 Plant 2 \$7 \$6 \$3 \$2 \$4 Plant 3 \$7 \$3 \$7 \$5 \$2 Plant 4 \$8 \$2 \$5 \$6 \$7 Amounts of sugar to buy (tons) Company 1 Company 2 Company 3 Company 4 Company 5 Total Demand Plant 1 0 0 0 0 0 0 420 Plant 2 0 0 0 0 0 0 360 Plant 3 0 0 0 0 0 0 400 Plant 4 0 0 0 0 0 0 375 Total 0 0 0 0 0 Available supply 350 250 200 300 500 Cost of sugar \$0 \$0 \$0 \$0 \$0 \$0 Cost of shipping \$0 \$0 \$0 \$0 \$0 \$0 Total cost \$0 Problem A cake-mix manufacturer has 4 different plants throughout the country. It can buy sugar from 5 different companies. The cost of the sugar and the transportation costs from each company to each plant are known. Where should the company buy sugar and how much should it buy, to meet the demand and minimize cost? Solution 1) The variables are the amounts of sugar to be bought from each company for each plant. On worksheet Purchase these are given the name Amounts_to_buy. 2) The constraints are simple and straightforward: Amounts_to_buy >= 0 via the Assume Non-Negative option Total_amounts_to_buy >= Demand Total_sold <= Supply 3) The objective is to minimize cost. This is defined as Total_cost on the worksheet. Remarks Even though this model is very simple, it is one of the most used models in the industry. It routinely saves many companies thousands or even millions of dollars a year.