PLEASE DO PART C ONLY. THE REST I HAVE INDICATED ANSWERS FOR EASIER WORK.

Comfort Plus Co. (CPI) manufactures a standard dining chair used in restaurants. The demand forecasts for quarter 1 (January-March) and quarter 2 (April-June) are 3,700 chairs and 4,200 chairs respectively. CPI has a policy of satisfying all demand in the quarter in which it occurs. The chair contains an upholstered seat that can be produced by CPI or purchased from DAP, a subcontractor. DAP currently charges 12.50 per seat, but has announced a new price of 13.75 effective April 1. CPI can produce the seat at a cost of 10.25. Seats that are produced, or purchase, in quarter 1 and used to satisfy demand in quarter 2 cost CPI 1.50 each to hold in inventory. CPIs seat-producing capacity is 3,800 seats per quarter. CPI cannot hold more than 300 seats in inventory from quarter to quarter.

Required:

Identify and define the decision variables

Ans

X₁ = no. of seats produced by CPI in quarter 1

X₂ = no. of seats purchased from DAP in quarter 1

X₃ = no. of seats carried in inventory from quarters 1 to 2

X₄ = no. of seats produced by CPI in quarter 2

X₅ = no. of seats purchased from DAP in quarter

Formulate the above problem as a linear programming model

Ans

Min Z=10.25X₁+12.5 X₂+1.5 X₃+10.25 X₄+13.75X₅ (Costs)

Subject to: X₁ + X₂ - X₃ 3,700 (quarter 1 demand)

X₃ + X₄ + X₅ 4,200 (quarter 2 demand)

X₁ 3,800 (CPIs production capacity in quarter 1)

X₄ 3,800 (CPIs production capacity in quarter 2)

X₃ 300 (Inventory capacity)

X₁, X₂, X₃, X₄, X₅ 0

(c) The model in (a) above was solved by the Management Scientist giving the following output:

What is the optimal solution including the optimal value of the objective function?

If the per-unit inventory cost increased from 1.50 to 2.50, would the optimal solution change? Would the optimal value of the objective function change?

If in quarter 2 CPIs per-seat production cost increased by 1.25 and DAP changed its mind about the announced price increase (thus leaving it at 12.50 per seat), would the optimal solution change?

If DAP reduced its per-seat selling price in quarter 1 from 12.50 to 12.25, should CPI purchase any seats in quarter 1?

How much is it worth to CPI to increase its inventory capacity from 300 seats o 400?