Answer Sheet - Formulate the Lp Model for This Problem

Answer Sheet - Homework 1

1.

(1) Formulate the LP model for this problem.

Variable:

X1:Numbers of Dog food to produce,

X2: Numbers of Cat food to produce

Objective: 4X1+5X2 (Max)

Constraint:

Meat: 4X1+5X2≤100

Soybean: 6X1+3X2≤120

Filler: 4X1+10X2≤160

Demand Limit: 0≤X1≤40, 0≤ X2≤30, X1 and X2 must be integers

(2) Solve the problem using the graphical method.

X1 and X2 must be integers,

Optimal solution: (X1=15, X2=8) or ( X1=10, X2=12), Maximal profit is $100.

2.

(1) Formulate the LP for this problem.

Variable:

X1: Acres of Corn to plant,

X2: Acres of Pumpkin to plant,

X3: Acres of Bean to plant

Objective: 2100X1+900X2+1050X3 (Max)

Constraint:

Irrigation Water: 2X1+3X2+X3≤50

Fertilizer: 500X1+400X2+300X3≤8000

Demand Limit: 0≤21000X1≤200000, 0≤10000X2≤180000, 0≤3500X1≤80000

Acres Limit: X1+X2+X3≤20

(2) Enter the numbers in the appropriate cells of ranges B12:D12 and E8:F12 in the Excel spreadsheet to solve this problem based on the (1) formulation.

A B C D E F

1 Farm Planning Problem

2

3 Corn Pumpkin Beans

4 Acres