Use the graphical method and substitution to find the solution. Show your steps on your scratchpaper.

Solve for the value of the objective function and the variables. Since the decision centers on the production of the two different cabinet models, we let

x = number of French Provincial cabinets produced each day

y = number of Danish Modern cabinets produced each day

Objective: Max $46x + $51y

subject to

Constraint #:

(1) 3x + 2y 300 hours (carpentry department)

(2) 2x + 2y <= 200 hours (painting department)

(3) 1x + 1y 150 hours (finishing department)

(4) x 40 units (contract requirement)

X, Y 0

a. what is the value of the objective function?

b. what is the value of x and y?

c. what is the slack for constraint #3?

d. what constraints #'s are binding?

Your Answer:

a) Value of the objective function? = $4,900

b) Value of x and y at optimum level x=40 and y=60

c.) Slack for constraint #3 =150-100 = 50

d.) The binding constraints are 3x + 2y 300 and 1x + 1y 150