1) Corporation wishes to buy at most 1800 units of a product. There are two kinds of the product M1 and M2 available. M1 occupies 2 ft³, cost $12 and company makes a profit of $3. M2 occupies 3 ft³, cost $15 and company makes the profit of $4. If budget is $15,000 and warehouse has 3000ft³ for the product,

(a) Set up the problem as a liner programming problem.

(b) Answer the problem graphically.

2) Solve the linear programming given below by using the simplex method:

Maximize:    Z = -X₁ + 2X₂
Subject to:        X₁ + 2X₂ ≤4
            2X₁ + 5X₂ ≤ 10
             X₁, X₂ ≥ 0

3) Solve the integer programming given below by using the Gomory’s plane algorithm:

Maximize: Z = X₁ + X₂
Subject to     : 2X₁ + X₂ ≤ 6
 4X₁ + 5X₂ ≤ 20
X₁,X₂ ≥ 0

4) Acme Manufacturing produces two products. Daily capacity of manufacturing process is 430 minutes. Product 1 needs 2 minutes per unit, product 2 needs 1 minute per unit. There is no limit on the amount produced o product 1, but maximum daily demand for product 2 is 230 units. The unit profit of product 1 is $2 and that of product 2 is $5. Determine the optimal solution by using dynamic programming.

5) Electro uses resin in its manufacturing process at a rate of 1000 gallons per month. It cost Elector $ 100 to place the order for the new shipment. Holding cost per gallon per month is $2, and the storage cost per gallon is $10. Historical data illustrates that demand during lead time is uniform over the range (0, 100) gallons. Find out the optimal ordering policy for Electro.

6) Describe PERT in detail with appropriate ex.