Answer to Question #174095 in Operations Research for Mimi

Question

1. The Munchies Cereal Company makes a cereal from several ingredients. Two of the ingredients,

oats and rice, provide vitamins A and B. The company wants to know how many ounces of oats

and rice it should include in each box of cereal to meet the minimum requirements of 48 mil-

ligrams of vitamin A and 12 milligrams of vitamin B while minimizing cost. An ounce of oats

contributes 8 milligrams of vitamin A and 1 milligram of vitamin B, whereas an ounce of rice

contributes 6 milligrams of A and 2 milligrams of B. An ounce of oats costs $0.05, and an ounce

of rice costs $0.03.

a. Formulate a linear programming model for this problem.

b. Solve this model by using graphical analysis.

2. What would be the effect on the optimal solution in (Question 1) if the cost of rice increased from

$0.03 per ounce to $0.06 per ounce?

Answer 1

x₁ is for rice, x₂ is for oats,

$\begin{cases} 6x_1+8x_2\geq 48,\\ 2x_1+x_2\geq 12; \end{cases}$

$f_1=0.03x_1+0.05x_2 \to min$

where x₁=8 and x₂=0,

$f_1=0.24 \text{}$ $;

$f_2=0.06x_1+0.05x_2\to min$

where x₁=4.8, x₂=2.4 and

$f_2=0.06\cdot 4.8+0.05\cdot 2.4=0.408~$ $