Dukes Computer Services assembles its own brand of personal computers from component parts it purchases overseas and domestically. DCS has enough regular production capacity to produce 160 computers per week. It can produce an additional 50 computers with overtime. The cost of assembling, inspecting, and packaging a computer during regular time is $190. Overtime production of a computer costs $260. Furthermore, it costs $10 per computer per week to hold a computer in inventory (estimated by averaging the beginning and ending inventory levels each week). DCS wants to meet all customer orders, with no shortages, to provide quality service. DCS's order schedule for the next 4 weeks is as follows: Week 1 2 3 4 Computer Orders 105 170 180 150 There are no computers in inventory at the beginning of the 4-week period. DCS wants to determine a schedule that will indicate how much regular and overtime production it will need each week to meet its orders at the minimum cost. The decision variables are provided for you: R = number of computers produced in regular time in week! OT = number of computers produced in overtime in week i Si = number of computers in inventory at the end of week i where i = 1, 2, 3, 4 You MUST use the variables described above in your answers to the questions. No credit if you make up new variables! Write the question number and your answer to the following: 1. Write the objective function. Do not simplify. 2. Write the conservation constraint for week 3. Do not simplify. Dukes Computer Services assembles its own brand of personal computers from component parts it purchases overseas and domestically. DCS has enough regular production capacity to produce 160 computers per week. It can produce an additional 50 computers with overtime. The cost of assembling, inspecting, and packaging a computer during regular time is $190. Overtime production of a computer costs $260. Furthermore, it costs $10 per computer per week to hold a computer in inventory (estimated by averaging the beginning and ending inventory levels each week). DCS wants to meet all customer orders, with no shortages, to provide quality service. DCS's order schedule for the next 4 weeks is as follows: Week 1 2 3 4 Computer Orders 105 170 180 150 There are no computers in inventory at the beginning of the 4-week period. DCS wants to determine a schedule that will indicate how much regular and overtime production it will need each week to meet its orders at the minimum cost. The decision variables are provided for you: R = number of computers produced in regular time in week! OT = number of computers produced in overtime in week i Si = number of computers in inventory at the end of week i where i = 1, 2, 3, 4 You MUST use the variables described above in your answers to the questions. No credit if you make up new variables! Write the question number and your answer to the following: 1. Write the objective function. Do not simplify. 2. Write the conservation constraint for week 3. Do not simplify
