Problema Solution
Elizabeth Lamulle takes vitamin pills. Each day she must have at least 16 units of Vitamin A, at least 5 units of Vitamin B1, and at least 20 units of Vitamin C. She can choose between red pills costing 10 cents each that contain 8 units of A, 1 of B1, and 2 of C; and blue pills that cost 20 cents each and contain 2 units of A, 1 of B1, and 7 of C. How many of each pill should she take in order to minimize her cost and yet fulfill daily requirements? What are the corners/vertices of the feasible region? Solve your problem.
Answer provided by our tutors
let
x = the number of red pills, x>=0
y = the number of blue pills, y>=0
8x + 2y >= 16
x + y >= 5
2x + 7y >= 20
the objective function is: F(x, y) = 10x + 20y gives the cost.
We need to find x and y, such that F(x, y) is minimum.
First draw the feasible region and find the vertices.
The feasible region is described by the system of inequalities:
8x + 2y >= 16
x + y >= 5
2x + 7y >= 20
x >=0
y >= 0
click here to see the graph of the feasible region:
the vertices are:
(10, 0), (3, 2), (1, 4), (0, 8)
F(10, 0) = 10*10 + 20*0 = 100
F(3, 2) = 10*3 + 20*2 = 70
F(1, 4) = 10*1 + 20*4 = 90
F(0, 8) = 10*0 + 20*8 = 160
F(x, y) has minimum for x = 3 and y = 2.
Thus Elizabeth Lamulle should buy 3 red and 2 blue pills.