Question

Linear programming

Answer 1

To prevent an infection, there are three drugs u, v, w needed. A patient must have at least 20 mg of u, 36 mg of v, 14 mg of w administered to heal. These drugs are commercially available in the form of A-pills and B-powders. An A-pill contains 1 mg of u, 2mg v and 3mg of w and costs 4 euros. A B-powder contains 5 mg of u, 6mg of v and 1mg of w and costs 5 euros. How many pills and powders must purchase a patient to cure as cheap as possible?

Answer 2

@.Sam.

Answer 3

@RadEn

Answer 4

constraints:
u >= 20
v >= 36
w >= 14

u = A+ 5B
v = 2A +6B
w = 3A+B

therefore:
A+5B >= 20
2A +6B >= 36
3A +B >= 14

graph these lines on an A,B coord grid

the region bounded by all 3 lines are points within constraints
max/min values will be at the intersection points
Cost = 4A +5B

find which intersection point yields lowest cost