The profit function for sales of two models of television sets at a chain discount store is given by where x is the number of sales per week of model A, and y is the number of sales per week of model B. Find and interpret the result.

The correct option is B) Px(10, 15) = 80

At a sales level of 10 units of model A and 15 units of model B, increasing sales of model A by one unit and holding sales of model B at 15 units will increase profit by approximately $80.

Explanation:

Note: This question is note complete. The complete question is therefore provided before answering the question as follows:

The profit function for sales of two models of television sets at a chain discount store is given by P(x, y) = 140x + 160y - 6x^2 + 4xy - 8y^2 - 500, where x is the number of sales per week of model A, and y is the number of sales per week of model B. Find Px(10, 15) and interpret the result.

A) Px(10, 15) = 120

At a sales level of 10 units of model A and 15 units of model B, increasing sales of model A by

one unit and holding sales of model B at 15 units will increase profit by approximately $120

B) Px(10, 15) = 80

At a sales level of 10 units of model A and 15 units of model B, increasing sales of model A by one unit and holding sales of model B at 15 units will increase profit by approximately $80.

C) Px(10, 15) = 140

At a sales level of 10 units of model A and 15 units of model B, increasing sales of model A by one unit and holding sales of model B at 15 units will increase profit by approximately $140

D) Px(10, 15) = 60

At a sales level of 10 units of model A and 15 units of model B, increasing sales of model A by one unit and holding sales of model B at 15 units will increase profit by approximately $60

The explanation to the answer is now given as follows:

Given;

P(x, y) = 140x + 160y - 6x^2 + 4xy - 8y^2 - 500 (1)

Taking partial differentiation of equation (1) with respect to x, we have:

Px(x, y) = 140 - 12x + 4y (2)

Since we are given Px(10, 15), it implies we substitutes for x = 10 and y = 15 into equation (2) and estimate as follows:

Px(10, 15) = 140 - (12 * 10) + (4 * 15)

Px(10, 15) = 140 - 120 + 60

Px(10, 15) = 80

Therefore, the correct option is B) Px(10, 15) = 80

At a sales level of 10 units of model A and 15 units of model B, increasing sales of model A by one unit and holding sales of model B at 15 units will increase profit by approximately $80.

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the answer is d

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