Question 101206
I will give one example:
You need atleast 140 mg of vitamin A and atleast 145 mg of vitamin B. A scoop of X food gives you 35mg of vit A and 30mg of vit B. A scoop of Y food gives you 30mg of vit A and 40mg of vit B. X food costs 8 dollars, but Y food costs 10 dollars. What is the minimum cost in order to attain all the essential vitamins.
a >= 140
a = 35x + 30y
35x + 30y >= 140
and
b >= 145
b = 30x + 40y
30x + 40y >= 145
and
x >= 0
and
y >= 0
{{{graph(400,400,-1,6,-1,6,(145 - 30x)/40,(140 - 35x)/30)}}}
Profit Equation: P(x,y) = 8x + 10y
P(0,14/3) = 0 + 10(14/3) = 140/3 = $46.67
P(29/6,0) = 8(29/6) + 0 = $38.67
P(2.5,1.75) = 8(2.5) + 10(1.75) = 20 + 17.5 = $37.5 .... Cheapest
2.5 scoops of x and 1.75 scoops of y