Product of x and y

A Company Manufactures Two Products X And Y. Each Product Has To Be Processed In Three

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?

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

A Poll showed that 25% of Americans are satisfied with the way things are going in the United States. Suppose a sample of 15 Americans is selected as part of a study of the state of the nation.

1. a) Compute the probability that exactly 5 of the 15 Americans surveyed are satisfied with the way things are going in the United States.

2. b) Compute the probability that at least 3 of the Americans surveyed are satisfied with the way things are going in the United States.

3. c) Compute the probability that no more than 4 of the Americans surveyed are satisfied with the way things are going in the United States.

4. d) Compute the probability that more than 2 but less than 6 of the Americans surveyed are satisfied with the way things are going in the United States.

5. e) Compute the expected value, variance, and standard deviation of the number of Americans who are satisfied with the way things are going in the United States.