Use Linear Programming to Solve Problems
-A doctor has told a sick patient to take vitamin pills. The patient needs at least 45 units of vitamin A, at least 11 units of vitamin $B$, and at least 37 units of vitamin $\mathrm { C }$. The red vitamin pills cost 10 \$ each and contain 6 units of $A , 1$ unit of $B$, and 2 units of $C$. The blue vitamin pills cost $20 c$ each and contain 4 units of $A , 1$ unit of $B$, and 5 units of $C$. How many pills should the patient take each day to minimize costs?
A) 6 red and 5 blue
B) 5 red and 6 blue
C) 11 red and 0 blue
D) 7 red and 4 blue

Question

Quizplus · Accepted Answer

To minimize costs while meeting the vitamin requirements, we set up the problem as a linear programming model. Let $x$ be the number of red pills and $y$ be the number of blue pills. The objective function to minimize is the cost: $10x + 20y$. The constraints from the vitamin requirements are: $6x + 4y \geq 45$ (for vitamin A), $x + y \geq 11$ (for vitamin B), and $2x + 5y \geq 37$ (for vitamin C). Solving this system, option A (6 red and 5 blue) is the combination that meets all requirements at the lowest cost.

Use Linear Programming to Solve Problems -A Doctor Has Told BBB

Use Linear Programming to Solve Problems
-A Doctor Has Told $B$