LP Formulation:

Given data:

Method Grade 6 Grade 8 Grade 10 Cost ($)

1

2

0.2

0.3

0.2

0.3

0.6

0.4

3.40

3.00
3 0.4 0.4 0.2 2.60

Let Wa,Wb,Aa and Ab be the pounds of wheat and alfalfa used to produce feed sold at discount price.

Let W1,W2,A1 and A2 be the pounds of wheat and alfalfa used to produce feed sold at non-discounted price.

The objective is to maximize Feedco’s profit.

Profit = (cost/lb) (pounds of wheat and alfalfa feed 1 sold at non-discounted price) + (cost/lb) (pounds of wheat and alfalfa feed 2 sold at non-discounted price) + (cost/lb) (pounds of wheat and alfalfa feed 1 sold at discounted price) + (cost/lb) (pounds of wheat and alfalfa feed 2 sold at discounted price) – (cost/lb) (total pounds of wheat purchased) – (cost/lb) (total pounds of alfalfa purchased)

Profit= 1.5(W1+A1)+1.3(W2+A2)+1.25(Wa+Aa)+1(Wb+Ab)−0.5(W1+W2+Wa+Wb)−0.4(A1+A2+Aa+Ab)

Thus, the objective function is,

Maximize

z= 1.5(W1+A1)+1.3(W2+A2)+1.25(Wa+Aa)+1(Wb+Ab)−0.5(W1+W2+Wa+Wb)−0.4(A1+A2+Aa+Ab)

The following constraints are,

Constraints 1: At most, 300lb of feed 1 can be sold.

(Pounds of wheat produce feed 1) + (Pounds of alfalfa produce feed 1) ≤300

Wa+Aa≤300

Constraint 2: At most, 300lb of feed 1 can be sold.

(Pounds of wheat produce feed 2) + (Pounds of alfalfa produce feed 2) ≤300

Wb+Ab≤300

Constraint 3: At most, 1000lb of wheat can be purchased.

(Pounds of wheat used to produce feed 1) + (Pounds of wheat used to produce feed 2) ≤1000

W1+W2+Wa+Wb≤1000

Constraint 4: At most, 800lb of alfalfa can be purchased

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