Please choose answer from the same sheet.. 1. R. C. Barker makes purchasing decisions for his company. One product that he buys costs \$50 per unit when the order quantity is less than 500. When the quantity ordered is 500 or more, the price per unit drops to \$48. The ordering cost is \$30 per order and the annual demand is 7,500 units. The holding cost is 10 percent of the purchase cost. If R. C. wishes to minimize his total annual inventory costs, he must evaluate the total cost for two possible ordering scenarios. What is the optimal order quantity for each scenario? (Round answer to nearest unit.)

200 and 306
306 and 500
300 and 306
300 and 500
None of the above
2. Consider the following linear programming problem:

Maximize 5x + 6y

Subject to 4x + 2y ≤ 420

1x + 2y ≤ 120

all variables ≥ 0 Which of the following points (X,Y) is not a feasible corner point?

(0, 60)
(105, 0)
(120, 0)
(100, 10)
(0, 0)
3. Andre Candess manages an office supply store. One product in the store is computer paper. Andre knows that 10,000 boxes will be sold this year at a constant rate throughout the year. There are 250 working days per year and the lead-time is 3 days. The cost of placing an order is \$30, while the holding cost is \$15 per box per year. How many units should Andre order each time?

 200 400 100 500 300

4. Consider the following linear programming problem:

Minimize 20x + 30y

Subject to 2x + 4y ≤ 800

6x + 3y ≥ 300

x, y ≥ 0

What is the optimum solution to this problem (X,Y)?

 (0, 0) (50, 0) (0, 100) (400,0) None of the above

5. Judith Thompson, the manager of the student center cafeteria, has added pizza to the menu. The pizza is ordered frozen from a local pizza establishment and baked at the cafeteria. Judith anticipates that weekly demand will be normally distributed with a mean weekly demand of 100 pizzas and standard distribution of 5 pizzas. The cafeteria is open 45 weeks a year, 5 days a week. The ordering cost if \$15 and the holding cost is \$0.40 per pizza per year. The pizza vendor has indicated that the lead-time for supply deliveries is normally distributed with a mean lead-time of 4 days and a standard deviation of 1 day. Judith wants to maintain safety stock based upon a 95% level of service. What is the optimal reorder point (round to nearest unit)?

88
117
54
00
None of the above

6. Average starting salaries for students using a placement service at a university have been steadily increasing. A study of the last four graduating classes indicates the following average salaries: \$30,000, \$32,000, \$34,500, and \$36,000 (last graduating class). Predict the starting salary for the next graduating class using a simple exponential smoothing model with alpha = 0.25. Assume that the initial forecast was \$30,000 (so that the forecast and the actual were the same).

 \$32,625 \$33,454 \$29,871 \$30,178

7. A tire dealership has sold an average of 1,000 radial tires each year. In the past two years, tire sales were as follows:

 Season Year 1 Demand Year 2 Demand Fall 200 250 Winter 350 300 Spring 150 165 Summer 300 285

Calculate the seasonal index for each quarter.

 Fall = 0.85, Winter = 1.25, Spring = 0.58, Summer = 1.12 Fall = 0.99, Winter = 1.19, Spring = 0.59, Summer = 1.17 Fall = 0.95, Winter = 1.35, Spring = 0.68, Summer = 1.22 Fall = 0.80, Winter = 1.20, Spring = 0.53, Summer = 1.07

8. Consider the following linear programming problem:

Maximize 5x + 6y

Subject to 4x + 2y ≤ 420

1x + 2y ≤ 120

All variables ≥ 0

Which of the following points (X,Y) is in the feasible region?

 (30, 60) (105, 5) (0, 210) (100, 10) None of the above

9. The following data reflects the number of cars sold at a local dealership over a ten-month period. Calculate the MAPE for months 4 through 10 using a three month moving average forecast.

 Time Period Number of Cars Sold 1 87 2 75 3 83 4 68 5 85 6 79 7 78 8 69 9 74 10 81 10.06% 8.14% 8.64% 9.51%

10. The annual demand for a product has been projected at 2,000 units. This demand is assumed to be normally distributed with a standard deviation of 2 units. The ordering cost is \$20 per order, and the holding cost is 20 percent of the purchase cost. The purchase cost is \$40 per unit. There are 250 working days per year. Whenever an order is placed, it is known that the entire order will arrive on a truck in 6 days (i.e., a constant lead-time). Currently, the company is ordering 500 units each time an order is placed. What level of service would require a reorder point of 60 units?

 37.21 47.99 78.61 84.13 92.45

11. Judith Thompson is the manager of the student center cafeteria. She is introducing pizza as a menu item. The pizza is ordered frozen from a local pizza establishment and baked at the cafeteria. Judith anticipates a weekly demand of 10 pizzas. The cafeteria is open 45 weeks a year, 5 days a week. The ordering cost is \$15 and the holding cost is \$0.40 per pizza per year. What is the optimal number of pizzas Judith should order (round to the nearest whole number)?

 92 184 211 174 300

12. The number of emergency calls received by the local 911 call center is as follows. Using trend projection to forecast the number of calls that will be received during week 11.

 Week Actual Value 1 50 2 35 3 25 4 40 5 45 6 35 7 20 8 30 9 35 10 20 22.54 24.16 22.00 23.00

13. Two models of a product Regular (X) and Deluxe (Y) are produced by a company. A linear programming model is used to determine the production schedule. The formulation is as follows:

Maximize profit 50x + 60y

Subject to 8x + 10y ≤ 800 (labor hours)

x + y ≤ 120 (total units demanded)

4x + 10y ≤ 500 (raw materials)

x,y ≥ 0

The optimal solution is X=100, Y=0. Which of these constraints is redundant?

 First constraint Second constraint Third constraint All of the above None of the above

14. Consider the following linear programming problem:

Maximize 4x + 10y

Subject to 3x + 4y ≤ 480

4x + 2y ≤ 360

all variables ≥ 0

The feasible corner points are (48,84), (0,120), (0,0), (90,0). What is the maximum possible value for the objective function?

1032
1200
1157
984
1498
15. Management has used seasonal variation time-series forecasting to calculate the following quarterly seasonal indices: 1.30, 0.90, 0.70, and 1.10. If the quarterly sales estimates for the next year are \$100,000, \$120,000, \$140,000, and \$160,000, calculate the seasonalized sales forecast for the third quarter.

 \$98,000 \$130,000 \$108,000 \$176,000

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