Homework 3 -1

Homework 3 Use the shells as the basis for solving the problems. Submit the workbook via Canvas by the assigned due date. 1. A customer requires during the next 4 months, respectively, 50, 65, 100, and 70 units of a commodity, and no backlogging is allowed (that is, the customer ’ s demand requirements must be met on time). Initial inventory is 20 units. Production costs are $5, $6, $4, and $7 per unit during these months. The storage cost from one month to the next is $2 per unit (assessed on ending inventory). It is estimated that each unit on hand in inventory at the end of month 4 could be sold for $6. Determine how to minimize the net cost incurred in meeting the demands for the next 4 months. Starting with the optimal solution above, use SolverTable to see what happens to the decision variables and the total cost when the initial inventory varies from 0 to 100 in 20-unit increments. How much lower would the total cost be if the company started with 40 units in inventory, rather than 20? Would this same cost decrease occur for every 20-unit increase in initial inventory? 2. A company faces the following demands during the next 3 weeks: week 1, 20 units; week 2, 10 units; week 3, 15 units. The unit production costs during each week are as follows: week 1, $13; week 2, $14; week 3, $15. A holding cost of $2 per unit is assessed against each week’s ending inventory. At the beginning of week 1, the company has 5 units on hand. In reality, not all goods produced during a week can be used to meet the current week’s demand. To model this fact, we assume that only half of the goods produced during a week can be used to meet the current week’s demands. The remaining weekly production can be used to meet future demand. Determine how to minimize the cost of meeting the demand for the next 3 weeks. 3. Woodco manufactures tables and chairs. Each table and chair must be made entirely out of oak or entirely out of pine. A total of 150 board feet of oak and 210 board feet of pine are available. A table requires either 17 board feet of oak or 30 board feet of pine, and a chair requires either 5 board feet of oak or 13 board feet of pine. Each table can be sold for $40, and each chair for $15. Determine how Woodco can maximize its revenue. 4. In the previous problem, suppose you want to investigate the effects of simultaneous changes in the selling prices of the oak and pine products. Specifically, you want to see what happens to the total revenue when the selling prices of oak products change by a factor 1 + k 1 and the selling prices of pine products change by a factor 1 + k 2 . Revise your model from the previous problem so that you can use SolverTable to investigate changes in total revenue as k 1 and k 2 both vary from -0.3 to 0.3 in increments of 0.1. Would you conclude that total revenue changes linearly within this range?