Most cake recipes have the basic ingredients of eggs, oil, flour, and milk. Susan just baked a cake, using 85% of the eggs, 73% of the oil, 78% of the flour, and 92% of the milk that she bought, by following the instructions from a recipe book that stated these restrictions:

■ The proportion of milk can be no more than 20%.

■ The proportion of eggs must be at least twice as much as the flour.

■ The proportion of oil must be at least 0.25 times as much as the flour.

■ The proportion of each ingredient must be at least 10%.

■ The proportion of flour must be at least 15%.

■ The proportions must sum to 1.0 and be nonnegative.

a. Develop a mathematical model that will yield a valid set of proportions to maximize the usage of the ingredients bought by Susan.

b. Implement your model on a spreadsheet and find an optimal solution using Solver.