Qs 1) Solve the following LP problem and perform sensitivity analysis:   Maximize P = 3x + 15y subject to : 2x + 4y ≤ 12                 5x + 2y ≤ 10 and x ≥ 0, y ≥ 0

Qs 1) Solve the following LP problem and perform sensitivity analysis:

Maximize P = 3x + 15y

subject to :

2x + 4y ≤ 12

                5x + 2y ≤ 10

and x ≥ 0, y ≥ 0.

Qs 2. Solve the following LP problem and perform sensitivity analysis:

Minimize C = 12x + 4y

subject to :

2x + 4y ≥ 12

                5x + 2y ≥ 10

and       x ≥ 0, y ≥ 0.

Qs 3. The production planner for Fine Coffees, Inc. produces two coffee blends: American (A) and British (B). He can only get 300 pounds of Colombian beans per week and 200 pounds of Dominican beans per week. Each pound of American blend coffee requires 12 ounces of Colombian beans and 4 ounces of Dominican beans, while a pound of British blend coffee uses 8 ounces of each type of bean. Profits for the American blend are $2.00 per pound, and profits for the British blend are $1.00 per pound. The goal of Fine Coffees, Inc. is to maximize profits. Solve the LP problem in Excel and also perform sensitivity analysis.

Qs 4 Solve the following transportation problem to minimize the cost.

TRANSPORTAION COST PER UNIT

Qs 5. Consider the following algebraic formulation of a cos-benefit-trade-off problems involving three benefits, where the decisions to be made are the levels of four activities:

Minimize cost C = 2A1 + A2 – A3 + 3A4

Subject to:

Benefit 1: 3A1 + 2A2 – 2A3 + 5A4 >= 80

Benefit 2: A1 – A2 + A4 >= 10

Benefit 3: A1 +A2 – A3 + 2A4 >= 30

A1, A2, A3 >= 0