Linear Programming Applied Please make this an original stor

Linear Programming Applied (Please make this an original story)

Due Sunday, September 27

1. Make up and describe a business situation that could be solved using linear programming. (5 points)

2. Identify and describe the two variables you are solving for. (5 points)

3. Write out all the inequalities defining the restrictions on those variables.   (5 points)

4. Describe and construct the equation defining the objective function (what you are trying to maximize or minimize). Example: profit, revenues, cost, etc. (3 points)

*Spelling, grammar and general appearance (2 points)

Solution

A manager at an Oil company wants to find the optimal mix of two blending processes.

Profit per operation

Process P1 = $4000

Process P2 = $5000

Maximum availability of Crude Oil

Grade A = 500 units

Grade B = 400 units

Minimum demand for gasoline

X = 300 units

Y = 200 units

Decision variables

X1 = No. of operations of P1

X2 = No. of operations of P2

Constraints

6X1 + 5X2 < 500

4X1 + 6X2 < 400

6X1 + 5X2 > 300

9X1 + 5X2 > 200

X1, X2 > 0

Objective function

Maximize Z = 4000X1 + 5000X2