Creative sports design (CSD) manufactures a standard size racket and an over sized racket. The firm's rackets are extremely light due to the use of a magnesium- graphite alloy that was invented by the firm's founder. Each standard size racket uses 0.125 kilograms of the alloy and each oversize racket uses 0.4 kilograms; over the next two week production period only 80 kilograms of the alloy are available. Each standard size racket uses 10 min. of manufacturing timeand each oversize racket uses 12 min. The profit contributions are $10 for each standard size racket and $15 for each oversized racket, and 40 hours of manufacturing time are available each week. Managment specified that at least 20% of the total production must3 be the standard size racket. How many rackets of each type should CSD manufacture over the next 2 weeks to maximize the total profit contributions? Assume that because of the unique nature of their products, CSD can sell as many rackets as they can produce?

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Asked Jan 18, 2019
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Creative sports design (CSD) manufactures a standard size racket and an over sized racket. The firm's rackets are extremely light due to the use of a magnesium- graphite alloy that was invented by the firm's founder. Each standard size racket uses 0.125 kilograms of the alloy and each oversize racket uses 0.4 kilograms; over the next two week production period only 80 kilograms of the alloy are available. Each standard size racket uses 10 min. of manufacturing timeand each oversize racket uses 12 min. The profit contributions are $10 for each standard size racket and $15 for each oversized racket, and 40 hours of manufacturing time are available each week. Managment specified that at least 20% of the total production must3 be the standard size racket. How many rackets of each type should CSD manufacture over the next 2 weeks to maximize the total profit contributions? Assume that because of the unique nature of their products, CSD can sell as many rackets as they can produce?

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Expert Answer

Step 1

Let us consider the 2 week production period together to build our model. Let us assume SS be the number of standard rackets produced and OS be the number of over-sized rackets produced.

Alloy material constraint:

0.125 x SS + 0.4 x OS <= 80

Manufacturing time constraint (in min):

10 x SS + 12 x OS <= 40 x 2 x 60

SS production percentage constraint:

SS >= 0.2 x (SS+OS) i.e. 0.8 x SS – 0.2 x OS >= 0

The objective function of the model is the total profit contribution given as:

Maximize (total profit contribution = 10 x SS + 15 x OS)

Step 2

Using the above model and solving it as a Linear Integer Programming (IP) problem on an LP solver such as MS-Excel ® or IBM CPLEX ® we get, the following solution:

SS = 46, OS = 185 a...

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