Suppose that each unit of production requires one hour of time on the production line.The variable production cost each week is as follows:
$10 per hour for each hour up to 40 hours (first shift)
$14.50 per hour for each hour from 40 to 80 hours (second shift)
$18.25 per hour for each hour from 80 to 120 (third shift)
The firm can build and hold inventory: that is, production in one week can be used to meet demand in future weeks.But all demand must be met, and no backordering is allowed. The holding cost for inventory is $1 per unit per week. The inventory at the end of twelve weeks should be zero. The inventory at start of week 1 is also zero.
Determine a production schedule that minimizes the variable production cost and inventory holding cost that meets all of the demand.
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