Problem 1 (40 points). A company produces two kinds of products. Producing one product of the...

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Problem 1 (40 points). A company produces two kinds of products. Producing one product of the first type requires 1/5 hours of assembly labor, 1/6 hours of testing, and $1.5 worth of raw materials. This type of product is sold at $9.3 each. Producing one product of the second type requires 1/4 hours of assembly, 1/4 hours of testing, and $1.4 worth of raw materials. This type of product is sold at $8.5 each. Currently, the company can provide at most 90 hours of assembly labor and 80 hours of testing every day. (1). If the company wants to maximize its daily profit, how should they formulate the problem as a linear optimization problem? (Ignore the integrality requirements of the product numbers.) (2). Write down the standard form of the LP you formulated in part (1). (3). Suppose the company can outsource up to 30 hours of overtime assembly labor and 20 hours of testing labor at a cost of $5 per hour. That is, if the 90 hours of assembly labor and 80 hours of testing labor is not enough, the company can pay someone else outside the company to help completing the labor. In this situation, how can we incorporate this into the our previous LP formulation? Problem 1 (40 points). A company produces two kinds of products. Producing one product of the first type requires 1/5 hours of assembly labor, 1/6 hours of testing, and $1.5 worth of raw materials. This type of product is sold at $9.3 each. Producing one product of the second type requires 1/4 hours of assembly, 1/4 hours of testing, and $1.4 worth of raw materials. This type of product is sold at $8.5 each. Currently, the company can provide at most 90 hours of assembly labor and 80 hours of testing every day. (1). If the company wants to maximize its daily profit, how should they formulate the problem as a linear optimization problem? (Ignore the integrality requirements of the product numbers.) (2). Write down the standard form of the LP you formulated in part (1). (3). Suppose the company can outsource up to 30 hours of overtime assembly labor and 20 hours of testing labor at a cost of $5 per hour. That is, if the 90 hours of assembly labor and 80 hours of testing labor is not enough, the company can pay someone else outside the company to help completing the labor. In this situation, how can we incorporate this into the our previous LP formulation?

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