Question

A Rancher is mixing two types of food, Brand X and Brand Y for his cattle. If each serving is required to have 60 grams of protein and 30 grams of fat, where Brand A has 15 grams of protein and 10 grams of fat and costs 80 cents per unit, and Brand B contains 20 grams of protein and 5 grams of fat, and cost 50 cents per unit, how much of each type should be used to minimize cost to the Rancher? a. Formulate a linear Programming model for this problem b. Solve this method by using Solver method

Answer 1

Answer:

$\left \{ {{15Q_a + 20Q_b = 60} \atop {10Q_a + 5Q_b = 30}} \right.$

Brand A Q 2.4

Brand B Q 1.2

Explanation:

Using Excel solver:

contrains:

c4 = 60

d4 = 30

solve e4 for min

variable cell b2:b3

a              b        c          d         e

              Q Protein Fat Cost

Brand A 2.4 36         24 1.92

Brand B 1.2 24           6 0.6

                       60         30 2.52

Protein = 60

Fat = 30