Math Problem Solver

A manufacturer provides specialized microchips. During the next 3 months, its sales, costs, and

available time are

Month 1 Month 2 Month 3

Chips required at the end of the month 1000 2500 2300

Cost - regular time ($/chip) 105 110 113Cost - over time ($/chip) 110 120 125

Storage cost ($/chip/month) 10 5 5Regular operation time (hr/month) 2625 2625 2625Maximum Overtime operation (hr/month) 480 480 480There are no chips in stock at the beginning of the first month. It takes 1.5 hr of production to produce a chip. The cost to store a chip starts from the beginning of one month to the next (i.e., if a chip is produced in month 1, regardless the date of the month, storage fee will be charged from beginning of month 1). Determine a production schedule and the total cost that meets the demand requirements, does not exceed the monthly production time limitations, and minimizes cost. Note that no chips should be in stock at the end of the 3 months.