A company manufactures two products X and Y. Each product has to be processed in three departments: welding, assembly and painting. Each unit of X spends 2 hours in the welding department, 3 hours in assembly and 1 hour in painting. The corresponding times for a unit of Y are 3, 2 and 1 hours respectively. The employee hours available in a month are 1,500 for the welding department, 1,500 in assembly and 550 in painting. The contribution to profits are $100 for product X and $120 for product Y.

1. Which one is one of the decision variables for this problem?

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a. X: Hours spent for product X

b. X: Quantity to be produced for product X

c. X: Profit (contribution) margin for product X

d. None

2. Total profits are maximized when the objective function (as a straight line on a graph) is:

a. Nearest to the origin irrespective of the ‘feasible region’

b. Nearest to the origin and tangent to the ‘feasible region’

c. Furthest from the origin and tangent to the ‘feasible region’

d. Furthest from the origin irrespective of the ‘feasible region’

3. What is the equation of the labor constraint line for the welding department in this linear model?

a. 2X + 3Y = 1,500 hours

b. 3X + 2Y = 550 hours

c. 2X + 3Y = 550 hours

d. 3X + 2Y = 1,500 hours

4. What is the solution to this linear programming problem in terms of the respective quantities of X and Y to be produced if profits are to be maximized?

a. X = 0, Y = 500

b. X = 150, Y = 400

c. X = 400, Y = 150

d. X = 550, Y = 0

e. None

5. Which resource (constraint) is not bounding the feasible region?

a. Welding

b. Assembly

c. Paint

d. All Bounding


6. Welding, Assembly, and Paint availability hours are extended by 10% (added overtime) and problem is solved again. Following screen shot shows the MS Excel solver solution after this change. What is the value of Objective (Z)?

a. 65,000

b. 66,300

c. 67,600

d. 68,900

e. 69,300

7. Utilizing the initial given data if management wants to increase the profit more what would you recommend?

a. Increase available hours for Welding

b. Increase available hours for Paint

c. Reduce hours needed to weld for X and/or Y

d. All above can be proposed

e. None of these can be proposed

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