What is the optimal order quantity for each scenario? (Round answer to nearest unit.)
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?
|
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?
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