2.10 Scheduling Tire Production: The Seaboch Tire Company produces four lines of tires: the economy, the glass-belted, the snow, and the radial tire. The problem it faces is to schedule two shifts of production during the last quarter of the calendar year. The production process primarily involves the use of vulcanization, fabrication, and plastometer equipment, but the limiting resource is the availability of the vulcanization machines. The four tires require different amounts of time at vulcanization, as tabulated below. Tire Hours/tire Econ. Glass Snow Radial 4.5 5 5.5 6 A sales forecast is available, breaking down predicted sales (in thousands) by tire type and by month. Sales October November December Econ. 8 7 6 Glass 18 16 18 Snow 4 15 Radial 5 15 8 In addition, the number of hours of vulcanizing time (in thousands), for each shift and for each month, is also known. October October November November December December Shift 1 2 1 2 1 2 Hours 110 100 130 120 120 115/nThe labor cost of operating the vulcanizing machines is $10 per hour during the first shift and $12 per hour during the second shift. The other relevant cost is storage: It costs $4 per month for storage and handling at the warehouse, regardless of tire type. This cost is incurred when production is scheduled in advance of demand to ensure that demand is met on time. (a) What production plan will minimize cost and meet demand at Seaboch Tire? 201 (b) How would the solution in (a) change if sales for each tire in December were 10% higher?

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