Q1: Comfort Plus Inc. (CPI) manufactures a standard dining chair used in restaurants. The demand forecasts for quarter 1 (January - March) and quarter 2 (April - June) are 3700 and 4200 chairs, respectively. CPI has a policy of satisfying 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 produced 3800 seats per quarter at a cost of $10.25 per seat.

Seats that are produced or purchased in quarter 1 and used to satisfy demand in quarter 2 cost CPI $1.50 each to hold in inventory, but the maximum inventory cannot exceed 300 seats.

Formulate a linear program to help minimize cost while satisfying demand. Solve the LP using Solver or LINDO and generate the range sensitivity analysis as part of the output.

Q2: After reading about the simplex method and watch the prescribed videos, complete the following problem.

Giapetto's Woodcarving, Inc. manufactures two types of toys: soldiers and trains. Each soldier sold generate $3 in profit while each train generates $2 in profit. The manufacture of wooden soldiers and trains requires two types of skilled labor: carpentry and finishing. A soldier requires 2 hours of finishing labor and 1 hour of carpentry labor. A train requires 1 hour of finishing labor and 1 hour of carpentry. Each week, Giapetto can obtain all the needed raw materials but only 100 finishing hours and 80 carpentry hours. Demand for trains is unlimited, but at most 40 soldiers are bought each week. Help Giapetto to maximize his profit.

a) Formulate the linear program

b) Solve the linear program graphically

c) Solve the linear program using the simplex method

d) Solve the linear program using Solver or LINDO