A small  rm specializes in making  ve types of spare automobile parts.Each part is  rst cast from iron in the casting shop and then sent to the  nishingshop where holes are drilled, surfaces are turned, and edges are ground. Therequired worker-hours (per 100 units) for each of the parts of the two shops areshown below: Part 1 2 3 4 5Casting 2 1 3 3 1Finishing 3 2 2 1 1The pro ts from the parts are 30, 20, 40, 25, and 10 (per 100 units), respec-tively. The capacities of the casting and  nishing shops over the next month are700 and 1000 worker-hours, respectively. Formulate the problem of determiningthe quantities of each spare part to be made during the month so as to maximizepro t.

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A small  rm specializes in making  ve types of spare automobile parts.
Each part is  rst cast from iron in the casting shop and then sent to the  nishing
shop where holes are drilled, surfaces are turned, and edges are ground. The
required worker-hours (per 100 units) for each of the parts of the two shops are
shown below:

Part 1 2 3 4 5
Casting 2 1 3 3 1
Finishing 3 2 2 1 1
The pro ts from the parts are 30, 20, 40, 25, and 10 (per 100 units), respec-
tively. The capacities of the casting and  nishing shops over the next month are
700 and 1000 worker-hours, respectively. Formulate the problem of determining
the quantities of each spare part to be made during the month so as to maximize
pro t.

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