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BU3315: Module 2 Linear Programming Using Computers Solutions

Exercise 2.1

Lakeside Boatworks

1

Solve the following problems:

1. Analyze the given graph of a linear programming model with a single constraint and the objective

function:

Source: Taylor III, B.W. (2013). Introduction to Management Science (11th ed.). Pearson

Education, Inc.

Use the information given in the graph to answer the following questions:

a. Maximize Z = 30x1 + 50x2.

b. Determine the optimal solution point.

c. Determine the values by which the constraints c1 and c2 must decrease or increase in order to

change the current solution point shown in the graph to the other extreme point.

BU3315: Module 2 Linear Programming Using Computers Solutions

Exercise 2.1

Lakeside Boatworks

2

2. Lakeside Boatworks is planning to manufacture three types of molded fiberglass recreational

boats—a fishing (bass) boat, a ski boat, and a small speedboat. The estimated selling price and

variable cost for each type of boat are summarized in the following table:

Boat Variable Cost Selling Price

Bass $12,500 $23,000

Ski 8,500 18,000

Speed 13,700 26,000

Source: Taylor III, B.W. (2013). Introduction to Management Science (11th ed.). Pearson

Education, Inc.

The company has incurred fixed costs of $2,800,000 to set up its manufacturing operations and

begin production. Lakeside has also entered into agreements with several boat dealers in the region

to provide a minimum of 70 bass boats, 50 ski boats, and 50 speedboats. Alternatively, the company

is unsure of what the actual demand will be, so it has decided to limit production to no more than

120 of any one boat. The company wants to determine the number of boats that it must sell to

break even while minimizing its total variable cost.

a. Formulate a linear programming model for this problem.

b. Solve the linear programming model that you formulated.

Submission Requirements:

 Submit your response in a Microsoft Excel workbook.

 Show the detailed steps that you performed to solve the problem.

Evaluation Criteria:

The exercise will be evaluated using the Exercise rubric.