A patient takes vitamin pills. Each day he must have at least 720 IU of vitamin...

A patient takes vitamin pills. Each day he must have at least 720 IU of vitamin A, 21 mg of vitamin B1, and 40 mg of vitamin C. He can choose between pill 1, which contains 120 IU of vitamin A, 3mg of vitamin B1, and 5 mg of vitamin C, and pill 2, which contains 90 IU of vitamin A, 3 mg of vitamin B1, and 10 mg of vitamin C. Pill 1 costs 20 cents and pill 2 costs 60 cents. How many of each pill should he buy in order to minimize his cost? What is the minimum cost?

Solutions

Expert Solution

Mathematical formulation:

Let x1 be the number of vitamin pill 1

Let x2 be the number of vitamin pill 2

Objective function

Min Z = 20x1 + 60x2

Subject of constraints

120x1+ 90x2 >= 720

3x1 + 3x2 > = 21

5x1 + 10x2 > = 40

Non-negative constraints

x1,x2 >= 0

Graphical Method:

orchestra answered 1 year ago

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