Question

John, following a familiar pattern, has discovered a new diet; this one is based primarily, on meat. He must eat 1 ounce of fat with each 3 ounces of lean. Since cost is an important aspect of all-meat diet, he decides to find out how cheaply he can buy a nominal quantity – at least 10 pounds, say – of the right mixture of fat and lean, in order to try it out.

Dantzig’s Butcher Shop carries three kinds of meat which John is willing to eat. These contain, 1, 5 and 10 ounces of fat per pound and retail at $1.35, $0.85, and $0.65, respectively

Using Solver, setup and solve this optimization problem.

Hint: You want to minimize cost while changing the quantities (in pounds) of each of the three types of meat.

Hint: 1 pound = 16 oz of meat

Hint: Cost = SUMPRODUCT (Amount purchased for each meat, cost/pound for each meat)

Hint: Constraint 1: The sum of the number of pounds purchased has to equal 10

Hint: Constraint 2: You must have 3 ounces of lean with each ounce of fat. You want to compare the count of lean ounces purchased against 3*Fat ounces purchased

Hint: Lean ounces purchased =SUMPRODUCT(pounds purchased of each meat, lean ounces per pound for each meat). Fat ounces are similar.

Hint: the final cost is less than $10

Save all the Solver Reports

Answer the following Questions in your spread sheet on the same spreadsheet where you entered your data:

1. How much should John buy of each meat?
2. How much should John pay for the meat?

Answer 1

So the fat should be 1/3= 33.33% and the lean meat should be 66.66%. This means for every pound we should have 16/3 ounces of meat. The model is shown below

The formulas

The solver set up

The result

The optimal mix is to get 9.3 pound of meat 2, and 0.67 pound of meat 3. The total cost is $8.37