Solve the below product mix problem using LINGOs modeling language only.

The Weigelt Corporation has three branch plants with excess production capacity. Fortunately, the corporation has a new product ready to begin production, and all three plants have this capability, so some of the excess capacity can be used in this way. This product can be made in three sizes large, medium, and small that yield a net unit profit of $420, $360, and $300, respectively. Plants 1, 2 and 3 have the excess capacity to produce 750, 900 and 450 units per day of this product, respectively, regardless of the size or combination of sizes involved.

The amount of available in-process storage space also imposes a limitation on the production rates of the new product. Plants 1, 2 and 3 have 13,000, 12,000, and 5,000 square feet, respectively, of in-process storage space available for a days production of this product. Each unit of the large, medium, and small sizes produced per day requires 20, 15 and 12 square feet, respectively.

Sales forecasts indicate that if available, 900, 1,200, and 750 units of the large, medium, and small sizes, respectively, would be sold per day.

At each plant, some employees will need to be laid off unless most of the plants excess production capacity can be used to produce the new product. To avoid layoffs if possible, management has decided that the plants should use the same percentage of their excess capacity to produce the new product.

Management wishes to know how much of each of the sizes should be produced by each of the plants to maximize profit.

a) Develop a LINGO modeling language code that includes the data in the DATA section.

b) Repeat the above question but with data retrieval and storage from/to a spreadsheet. Construct a spreadsheet and modify the data section of the model so that it takes the data from and stores the result in that spreadsheet after the LINGO model is executed.

c) Provide the LINGO code for (a) and (b) above, the solution output in (a) and the excel spreadsheet in (b) with all information.