Lakeside boatworks is planning to manufacture

MAT540 Week 8 Discussion Problem 10

Name

Instructor Name

Course

University

Date

Practice setting up linear programming models for business applications

Select an even-numbered LP problem from the text, excluding 14, 20, 22, 36 (which are part of your homework assignment). Formulate a linear programming model for the problem you select

I have selected Problem Number 10

Problem 10

1. The Lakeside Boatworks is planning to manufacture three types of molded fiber glass 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

The company has incurred fixed costs of $2,800,000 to set up its manufacturing operation and begin production. Lakeside has also entered into agreement with several boat dealers in the region to provide a minimum of 70 bass boats, 50 ski boats, and 50 speed boats. Alternatively, the company is unsure of what 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 model using the computer

Solution

Here the objective function must be solved for value of z=0 as breakeven point is a no profit no loss situation. Thus, we will write the objective function for profit and then equate it to zero. While using Excel solver, chose the option value of (0) instead of min or max

Let x1 = No of Bass boats

x2 = No of ski boats

x3 = No of speed boats

The Objective function coefficient : Selling price - variable cost

Variable Objective function coefficient

x1 10500

x2 9500

x3 12300

Formulation:

As objective function is in terms of profit, we need to subtract the fixed costs from the total profit margin.

Minimize, z= 0 = 10500x1 + 9500x2 +12300x3 - 2800000

Subject to constraints

x1>=70 (Minimum requirement)

x2>=50 (Minimum requirement)

x3>=50 (Minimum requirement)

x1<=120 (Maximum)

x2<=120 (Maximum)

x3<=120 (Maximum)

x1, x2,x3>= 0 (Non negativity constraint)

x1

x2

x3

10500

9500

12300

120

50

86.6

0

1

0

0

120

>=

70

0

1

0

50

>=

50

0

0

1

86.6

>=

50

1

0

0

120.0

<=

120

0

1

0

50.0

<=

120

0

0

1

86.6

<=

120

Answer: Thus, to break even, Lakeside boat works must sell following no of units.

Boat

Number to be produced

Bass

120.0

Ski

50.0

Speed

86.6

Z

0

Reference

Taylor, B. M. (2010). Introduction to management science (10th ed.). Upper Saddle River, NJ:

Pearson/Prentice Hall.