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bikewheels

# bikewheels - each Assume that at these prices the firm can...

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Another Linear Programming Example: Bicycle Wheels Page 63 (27) Free Wheelers, Inc. makes spokes and rims for mountain bike wheels. Recently, the firm has also started selling assembled wheels. Each spoke requires 0.04 hours of machine time and 0.01 hours of labor, and costs \$0.05 to make. Each rim requires 0.6 hours of machine time and 0.5 hours of labor, at a cost of \$4.00. An assembled wheel requires one rim and 72 spokes. Assembling a wheel takes 1.2 hours of labor, in addition to that needed to make its rim and spokes; no further machine time is needed. The assembly process also incurs additional direct costs of \$11.00. Up to 378 hours of machine time and 267 hours of labor are available per week. Assembled wheels sell for \$50.00. Spokes not used to make assembled wheels can be sold for \$0.10 each. Similarly, rims not used in assembled wheels can be sold for \$10

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Unformatted text preview: each. Assume that, at these prices, the firm can sell all the products it can produce. Model without helpers Model with helpers x 1 = Number of spokes made x 1 = Number of spokes made x 2 = Number of rims made x 2 = Number of rims made x 3 = Number of wheels made x 3 = Number of wheels made Max : 0.1(x 1-72 x 3 )+10(x 2- x 3 ) +50 x 3 y 1 = Number of spokes sold-[0.05 x 1 +4 x 2 +11 x 3 ] y 2 = Number of rims sold S.T. y 3 = Number of wheels sold 0.4 x 1 +6 x 2 ≤ 378 Max: 0.1 y 1 +10 y 2 +50 y 3-[0.05 x 1 0.1x 1 +0.5 x 2 +1.2 x 3 ≤ 267 +4x 2 +11 x 3 ] x 1-72 x 3 ≥ 0 S.T. x 2- x 3 ≥ 0 0.4 x 1 +6 x 2 ≤ 378 x 1 , x 2, x 3 ≥ 0 0.1x 1 +0.5 x 2 +1.2 x 3 ≤ 267 y 1 = x 1-72 x 3 y 2 = x 2- x 3 y 3 = x 3 x 1 , x 2, x 3, y 1, y 2, y 3 ≥ 0...
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bikewheels - each Assume that at these prices the firm can...

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