Question

1-formulate this problem

2-code it using lingo ans write the optimal profit

3. Eeedceproduces two types of cattle feed, both consisting totally of wheat and alfalfa. Feed 1 must contain at least 80% wheat, and feed 2 must contain at least 60% alfalfa. Feed 1 sells for $1.50/lh, and feed 2 sells for $1.30/lb. Eeedce,can purchase up to 1,000 lk of wheat at 50c/h and up to 800, of alfalfa at 40¢/lb. Eeede,has decided to give its customer (assume it has only one customer) a quantity discount. If the customer purchases more than 300 lb of feed 1, each pound over the first 300 lh will sell for only $1.25/lb. Similarly, if the customer purchases more than 300 pounds of feed 2, each pound over the first 300 lb will sell for $1.00/lb. Formulate an LP to maximize Eeedce's profit

Answer 1

1. LP is formulated as follows:

Let

W1, W2 be the quantity (lb) of wheat used to make feed 1 and 2 resp.

A1, A2 be the quantity (lb) of Alfalfa used to make feed 1 and 2 resp.

F11 be the quantity of feed 1 sold without discount

F12 be the quantity of feed 1 sold with discount

F21 be the quantity of feed 2 sold without discount

F22 be the quantity of feed 2 sold with discount

Max 1.5F11+1.25F12+1.3F21+1F22-.5W1-.5W2-.4A1-.4A2

s.t.

W1+W2<=1000

A1+A2<=800

F11+F12-W1-A1=0

F21+F22-W2-A2=0

.2W1-.8A1>=0

-.6W2+.4A2>=0

F11<=300

F21<=300

F11,F12,F21,F22,W1,W2,A1,A2>=0

Solution using LINDO is following:

Lingo 17.0-Solution Report-Lingo! File Edit Solver Window Help Lindo Model - Lingo a3Solution Report - Lingo1 Global optimal solution found Objective value: Infeasibilities: Total solver iterationS: Elapsed runtime seconds: 1457.500 0.000000 2.73 LP S.t. W1+W2 <=1000 Model Class: A1+A2<-800 Fl1+F12-w1-A1-0 F21+F22-W2-A2-0 Total variables: Nonlinear variables: Integer variables: Total constraints: Nonlinear constraints: -·6H2 + . 4A2 >=0 F11<=300 F21<=300 Total nonzeros: 26 Nonlinear nonzeros: Value Variable F11 F12 F21 F22 W1 300.0000 950.0000 300.0000 250.0000 1000.000 0.000000 250.0000 550.0000 Reduced Cost 0.000000 0.000000 0.000000 0.000000 0.000000 0.3125000 0.000000 0.000000 Al A2 Row Slack or Surplus 1457.500 0.000000 0.000000 0.000000 0.000000 0.000000 220.0000 0.000000 Dual Price 1.000000 0.8125000 0.6000000 1.250000 1.000000 -0.3125000 0.000000 0.2500000 For Help, press F1 NUM Ln 23, Co

Optimal solution:

Variable 300.0000 950.0000 300.0000 250.0000 1000.000 0.000000 250.0000 550.0000 F12 F22 W1 A.1

Total profit = $ 1,457.5