Two of the ingredients oats and rice provide vitamins A and

Two of the ingredients, oats and rice, provide vitamins A and B. How many ounces of oats and rice it should include in each box of cereal to meet the minimum requirements of 45 milligrams of vitamin A and 13 milligrams of vitamin B while minimizing cost. An ounce of oats contributes 10 milligrams of vitamin A and 2 milligram of vitamin B, whereas an ounce of rice contributes 6 milligrams of A and 3 milligrams of B. An ounce of oats costs $0.06, and an ounce of rice costs $0.03.

a. Formulate a linear programming model for this problem.

b. Solve the model by using graphical analysis.

Thx

Solution

Let X ounces of oats and y ounces of rice be included in each box.

10x+6y>=45

and 2x+3y >= 13

Cost z= 0.06x+0.03y

Our objective is to minimize z

Corner points are (6.5,0) (3.167, 2.222) (0,7.5)

z value for first point = 0.39

For second point = 0.506725+0.06666

= 0.573391

For third point = 0.225

Subject to inclusion of all vitamins the optimal solution is second point.