Question

WF prepares and sells birdseed mixes to a variety of stores. Their Fancy product generates a contribution of $12 per 100 pound bag, and their Multigrain product has a contribution of $9 per 100 pounds.

The seed goes through 3 processing stages; mixing, sterilization and packaging. The time requirements for each batch of 100 bags of Fancy and 10,000 pounds of Multigrain (which is sold in bulk) is shown below:

                                                            Minutes Required

	Mixing	Sterilization	Packaging
Fancy	200	200	100
Multigrain	100	300	O (sold in bulk)
Minutes available	6,000	12,000	4,500

1. Using Solver, determine the optimal product mix.

2. What happens if the minutes available for mixing are doubled?

Answer 1

Fancy generates a profit of $12 per 100 pound bag. However, it is produced in a batch of 100 bags. This means each batch produces a profit of 100*12 = 1200 and each batch is 100*100 = 10000 pounds

Similarly multigrain has a contribution $9 per 100 pounds. However, it produced in 10000 pounds together. Thus the profit of each bulk of multigrain is 9*10000/100 = 900

a)

This will help us simplify the problem and create the model as shown below

The formulas are shown below

The solver parameters are shown below

The result is shown below. The total profit is 45000 by making 15 batches of 100 bags of Fancy and 30 units of 10000 pounds of multigrain.

b)

If we double the mixing minutes to 12000 the result is shown below. The profit will now be 63000. With fancy = 45 batches (100 bags each) and multigrain = 10 bulk units (10000 pounds each).