simplex method

A dairy farmer’s cows need three nutrients (A, B, and C) to subsist and produce milk each day.Each cow must receive the equivalent of 100 units of nutrient A, 200 units of nutrient B, and 50 unitsof nutrient C in order to maximize milk output. The farmer can use any combination of three feedsVI,12, and f3) in meeting these minimum requirements. The local feed dealer sells all three feeds, which have the following cost per pound and nutrient equivalents (for A, B, and C) per pound.
Feed
Nutrient per pound
Cost ($/pound)
A
B
C
f/
5
22
3
0.25
12
10
25
2
0.5
f3
7
12
5
0.27
Assume that the farmer’s objective is to minimize the cost per cow of buying any combination of these three feeds that satisfies the daily nutrient requirement of the cows.
a) Solve this problem using the simplex method.