Problem 1. A still company estimates the demand for steel as follows (in millions of tons per year): Millions of Tons 10 12 14 16 18 Probability .10 .25 .30 .20 .15 a. (0.3 points) If capacity is set at 18 million tons, how much of a capacity cushion is there? b. (0.2 points) What is the probability of idle capacity if capacity is set at 16 million tons? c. (0.5 points) If it costs $8 million per million tons of lost business and $80 million to build a million tons of capacity, which capacity level, among 10, 12, 14, 16, and 18, will minimize the total costs? Problem 2. Given the following demand forecasts, costs, and constraints for a company. Quarter Demand 1 5,000 2 8,200 3 10,500 4 4,300 Regular production capacity = 7,000 units/quarter Overtime capacity = 2,000 units/quarter Subcontracting capacity = 7,000 units/quarter Inventory capacity = 10,000 units/quarter Beginning inventory = 0 Regular production cost = $10/unit Overtime production cost = $14/unit Subcontract production cost = $18 /unit Inventory holding cost = $4 /unit/quarter Backorder cost = $5 /unit/quarter Assume backorders carry over to the next quarter, that is, you need to use this quarter's inventory to fulfill previous quarter's backorder. a. What is the total cost if the company uses a Level Production Strategy with Overtime and Subcontracting? Fill in the table below. Quarter Demand Production Inventory Overtime Subcontract 1 5000 2 8200 3 4 10500 4300 total cost b. What is the total cost if the company uses a Level Production Strategy with Backorders? Fill in the table below. Backorder can accumulate and carry over to next period. Quarter Demand 1 5000 2 8200 3 10500 4 4300 total cost Production Inventory Backorder c. What is the total cost if the company uses a Chase Demand Strategy with Subcontracting? (No need to consider hiring and/or firing) Fill in the table below. Quarter Demand Production Subcontract 1 5000 2 8200 3 10500 4 4300 total cost Problem 3. At the University Hospital, five blood samples must be scheduled through a blood-testing laboratory. Each sample goes through up to four different testing stations. The times for each test and the due dates for each sample are as follows: Sample Test Station/Hours Due Date (hours) 1 A/1, B/2, C/3, D/1 6 2 B/2, C/3, A/1, D/4 10 3 C/2, A/3, D/1, C/2 8 4 A/2, D/2, C/3, B/1 14 5 D/2, C/1, A/2, B/4 12 a. Using a Gantt chart, schedule these five samples in priority order of earliest due date first. What is the make span? b. Assume that the capacity of each test station (A, B, C, and D) is doubled. Prepare an FCS for this situation. Problem 4. A secretary is considering three dispatching rules for typing term papers. The following information is given on jobs that are waiting to be typed: Hours until Due Total Remaining Processing Paper Date Time* (hours) Processing Time (typing hours) Arrival Order of ABCDE 20 12 10 4th 19 15 12 16 11 D 10 5 E 18 11 2657 3d 2d 1st 5th *Includes typing, corrections, and copying. Use the following dispatching rules to determine the sequence for term paper processing. a. SPT b. FCFS c. CR