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# Kite 'N String: Maximum Profit Using Linear Programming

Kite 'N String manufacture old-fashioned diagonal and box kites from high-strength paper and wood. Each diagonal kite nets the company a \$3 profit, requires 8 square feet of paper and 5 feet of wood. Each box kite nets \$5, requires 6 square feet of paper and 10 feet of wood. Each kite is packaged in similar containers. This week Kite 'N String have 1500 containers, 10000 square feet of paper and 12000 feet of wood.

a) How many of each type should Kite 'N String make to maximize profit? What is the maximum profit?
b) Which constraint(s) is/are binding?
c) If an additional 2000 square feet of paper is available, how many of each type to make to maximize profit? What is the maximum profit?
d) Which constraint(s) is/are binding for part 3?

#### Solution Preview

a) How many of each type should Kite 'N String make to maximize profit? What is the maximum profit?
b) Which constraint(s) is/are binding?

Using regular arrangement of data:
Paper (in square feet) Wood (in in square feet) Profit
Diagonal kite (x) 8x 5x 3x
Box Kite (y) 6y 10y 5y
Total 10000 12000
Maximize: 3x + 5y
subject to: 8x + 6y = 10000
5x + 10y = 12000

Using ...

#### Solution Summary

This is a linear programming problem on the optimum number of each kind of kites to make to maximize profits. The problem solution is contained in the attached Excel file using Excel Solver.

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