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 units of nutrient C in order to maximize milk output. The farmer can use any combination of three feeds ( f1, f2, 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.
Nutrient Content Per Pound
|
Feed
|
A
|
B
|
C
|
($/pound)
|
|
f1
|
5
|
22
|
3
|
0.25
|
|
f2
|
10
|
25
|
2
|
0.50
|
|
f3
|
7
|
12
|
5
|
0.27
|
|
|
Cost
Assume that the farmer's objective is to minimize the cost per cow of buying any com- bination of these three feeds that satisfy the daily nutrient requirements of the cow.
a. Write the standard form of this LP problem.
b. Solve this problem using the simplex method.