# Question

The Dorwyn Company has two new products that will compete with the two new products for the Wyndor Glass Co. (described in Sec. 3.1). Using units of hundreds of dollars for the objective function, the linear programming model shown below has been formulated to determine the most profitable product mix.

Maximize Z = 4x1 + 6x2,

subject to

x1 + 3x2 ≤ 8

5x1 + 2x2 ≤ 14 and

x1 ≥ 0, x2 ≥ 0.

However, because of the strong competition from Wyndor, Dorwyn management now realizes that the company will need to make a strong marketing effort to generate substantial sales of these products. In particular, it is estimated that achieving a production and sales rate of x1 units of Product 1 per week will require weekly marketing costs of x13 hundred dollars. The corresponding marketing costs for Product 2 are estimated to be 2x22 hundred dollars. Thus, the objective function in the model should be Z = 4x1 + 6x2 – x13 – 2x22.

Dorwyn management now would like to use the revised model to determine the most profitable product mix.

Maximize Z = 4x1 + 6x2,

subject to

x1 + 3x2 ≤ 8

5x1 + 2x2 ≤ 14 and

x1 ≥ 0, x2 ≥ 0.

However, because of the strong competition from Wyndor, Dorwyn management now realizes that the company will need to make a strong marketing effort to generate substantial sales of these products. In particular, it is estimated that achieving a production and sales rate of x1 units of Product 1 per week will require weekly marketing costs of x13 hundred dollars. The corresponding marketing costs for Product 2 are estimated to be 2x22 hundred dollars. Thus, the objective function in the model should be Z = 4x1 + 6x2 – x13 – 2x22.

Dorwyn management now would like to use the revised model to determine the most profitable product mix.

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