Problem 1
Grear Tire Company has produced a new tire with an estimated mean lifetime mileage of 36,500 miles. Management also believes that the standard deviation is 5000 miles and that tire mileage is normally distributed. Use a worksheet to simulate the miles obtained for a sample of 500 tires.
a) Use the Excel COUNTIF function to determine the number of tires that last longer than 40,000 miles. What is your estimate of the percentage of tires that will exceed 40,000 miles?
b) Use COUNTIF to find the number of tires that obtain the mileage less than 32,000 miles. Then, find the number with less than 30,000 miles and the number with less than 28,000 miles.
c) If management would like to advertise a tire mileage guarantee such that approximately no more than 10% of the tires would obtain mileage low enough to qualify for the guarantee, what tire mileage considered in part b) would you recommend for the guarantee?
Problem 2
The L. Young & Sons Manufacturing Company produces two products, which have the following profit and resource requirement characteristics.
Characteristic Product 1 Product 2
|
Profit/unit
|
$4
|
$2
|
|
Dept. A hours/unit
|
1
|
1
|
|
Dept. B hours/unit
|
2
|
5
|
Last month's production schedule used 350 hours of labor in department A and 1000 hours of labor in department B. Young's management has been experiencing workforce morale and labor union problems during the past 6 months because of monthly departmental workload fluctuations. New hiring, layoffs, and interdepartmental transfers have been common because the firm has not attempted to stabilize workload requirements.
Management would like to develop a production schedule for the coming month that will achieve the following goals.
Goal 1: Use 350 hours of labor in department A. Goal 2: Use 1000 hours of labor in department B. Goal 3: Earn a profit of a least $1300.
a. Formulate a goal programming model for this problem, assuming that goals 1 and 2 are P1 level goals and goal 3 is a P2 level goal: assume that goals 1 and 2 are equally important.
b. Solve the model formulated in part (a) using the graphical goal programming procedure.
c. Suppose that the firm ignores the workload fluctuations and considers the 350 hours in department A and the 1000 hours in department B as the maximum available. Formulate and solve a linear programming problem to maximize profit subject to these constraints.
d. Compare the solutions obtained in parts (b) and (c). Discuss which approach you favor, and why.
Problem 3
Michigan Motors Corporation (MMC) has just introduced a new luxury-touring sedan. As part of its promotional campaign, the marketing department has decided to send personalized invitations to test drive the new sedan to two target groups: (1) current owners of an MMC luxury automobile and (2) owners of luxury cars manufactured by one of MMC's competitors. The cost of sending a personalized invitation to each customer is estimated to be $1 per letter. Based on previous experience with this type of advertising, MMC estimates that 25% of the customers contacted from group 1 and 10% of the customers contacted from group 2 will test drive the new sedan. As part of this campaign, MMC has set the following goals.
Goal 1: Get at least 10,000 customers from group 1 to test drive the new sedan. Goal 2: Get at least 5000 customers from group 2 to test drive the new sedan. Goal 3: Limit the expense of sending out the invitations to $ 70,000.
Assume that goals 1 and 2 are P1 priority level goals and that goal 3 is a P2 priority level goal.
a. Suppose that goals 1 and 2 are equally important; formulate a goal programming model of the MMC problem.
b. Use the goal programming computer procedure illustrated in section 14.2 to solve the model formulated in part (a). Enclose the EXCEL output sheets.
c. If management believes that contacting customers from group 2 is twice as important as contacting customers from group 1, what should MMC do?