The Skimmer Boat Company manufacture three kinds of molded fiberglass recreation

Question

The Skimmer Boat Company manufacture three kinds of molded fiberglass recreational boats- a bass fishing boat, a ski boat, and a speedboat. The profit for a bass boat is $20, 500, the profit for a ski boat is $12,000, and the profit for a speedboat is $22, 300. The company believes it will sell more bass boats than the other two boats combined but no more than twice as many. The ski boat is its standard production model, and bass boats and speedboats are modifications. The company has production capacity to manufacture 210 standard (ski-type) boats; however, a bass boat requires 1.3 times the standard production capacity, and a speedboat requires 1.5 times the normal production capacity. In addition, a bass boat uses one high-powered engine and a speedboat uses two, and only 160 high-powered engines are available. The company wants to know how many boats of each type to produce to maximize profit Formulate and solve an integer programming model for this problem.

Explanation / Answer

x1 = bass fitting boad;

x2 = ski boat;

x3 = speed boat;

Maximize profit = 20500x1+12000x2+22300x3;

under given constraints:

x1>= x2+x3;

2(x2+x3)>=x1;

1.3x1+x2+1.5x3 <=210;

x1+x2+2x3 <=160;

We will use branch and bound method;

First ignore the integer constraint;

we get the solution to above equations as

x1=106.667; x2 = 53.333; x3 = 0 ;

now we add another constraint that;

x1>=107 and x1<=106

we get solution for x<=106 as x1=106 and x2 =54 and x3=0;

and profit = 2821000;

now solving for x1 >=107;

we dont find any valid solution for this;

so our integer solutions to above equations are x1 =106;

x2 = 54

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