Grandma’s Little Bakery is trying to figure out how much grain to order for the next month to mix into its most favorite flourless multi-grain bread. The grains that can be bought from local suppliers have the following composition and price:

In order for the dough to bake smoothly, the amount of starch in the mixture should be kept within 20 to 30 percent. Because of taste considerations, the amount of grain #2 in the mix cannot exceed 20%. Finally, for proper nutritional balance, the mixture should have at least 15% protein, at least 40% fiber, and no more than 12% gluten.

To satisfy the demand for next month, the bakery needs to produce exactly 150 kilograms of multi-grain dough mix. Help Mama’s Little Bakery find the least costly mix of grains that will satisfy demand.

a. Formulate the problem as a linear program (i.e., define the variables, and write down the objective function and all constraints in algebraic form).

b. Create a spreadsheet model for this problem and solve it with Solver.

c. What is the optimal solution? What is the optimal value?