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

Formulate a linear programming model for this problem.

Solve the model by using the computer.

x = bass boat; boat; z= speed boat

23,000x + 18,000y + 26,000z = 12,500x + 8,500y + 13,700z + 2,800,000

10,500x+ 9,500y + 12,300z = 2, 800, 000

Minimize Z= 12,500x + 8,500y + 13,700z

Subject to 10,500x + 9,500y + 12,300z = 2,800,000

X=> 70 X<

Y=>50 Y<

Z=>50 Z<

X, y, z =>0

TC=$2,925,284.55

Can you have me understand how to get the total cost , break the problem down