Answer:
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.
