Question

The Skimmer Boat Company manufactures the Water Skimmer bass fishing boat. The company purchases the engines it installs in its boats from the Mar-gine Company, which specializes in marine engines. Skimmer has the following production schedule for April, May, June, and July:

Month Production
April 60
May 85
June 100
July 120
Mar-gine usually manufactures and ships engines to Skimmer during the month the engines are due. However, from April through July, Mar-gine has a large order with another boat customer, and it can manufacture only 40 engines in April, 60 in May, 90 in June, and 50 in July. Mar-gine has several alternative ways to meet Skimmer’s production schedule. It can produce up to 30 engines in January, February, and March and carry them in inventory at a cost of $50 per engine per month until it ships them to Skimmer. For example, Mar-gine could build an engine in January and ship it to Skimmer in April, incurring $150 in inventory charges. Mar-gine can also manufacture up to 20 engines in the month they are due on an overtime basis, with an additional cost of $400 per engine. Mar-gine wants to determine the least costly production schedule that will meet Skimmer’s schedule. Formulate a linear programming model and solve using the computer (Excel Solver).

Answer 1

A linear programming model for Mar-gine Company's engine production includes decision variables for production, inventory, and overtime, minimizing costs while meeting Skimmer's boat production needs, subject to production and capacity constraints.

Step-by-step explanation:

The question requires the creation of a linear programming model to determine the least costly production schedule for Mar-gine Company to meet Skimmer Boat Company's production needs. Plant 1 can produce 200 pairs of skis or 100 snowboards per month if dedicated to one product, but has flexibility to produce both simultaneously. The goal is to find an optimal mix of inventory and overtime to fulfill the production schedule at the lowest cost, factoring in inventory charges and overtime costs. This problem can be solved using Excel Solver, a tool in Excel that optimizes linear programming models.

To create this model in Excel, define decision variables for regular production, inventory holding, and overtime production for each month. Objective function would minimize total costs, including production, inventory, and overtime. Constraints should ensure production meets demand, and should not exceed monthly production capacities or inventory and overtime limits. This model is a practical application of linear programming in operations management.