Solve the problem.
-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 Px(10, 15) and interpret the result.
A) 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
B) 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) 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
D) 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

Question

Solve the problem.
-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 Px(10, 15) and interpret the result.
A) 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 
B) 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) 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 
D) 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

Quizplus · Accepted Answer

To find Px(10,15), we need to substitute x = 10 and y = 15 into the profit function. Therefore, Px(10,15) = 11ebb6d7_4897_be18_b437_09b4d6160b85_TB8593_11. To interpret the result, we need to calculate the partial derivative of the profit function with respect to x at (10,15), which is 4. This means that increasing sales of model A by one unit at the current sales level of 10 units of model A and 15 units of model B will increase profit by approximately $80. Thus, choice B is the correct option. Plugging in x=10 and y=15 into the given profit function, we get 
P(10,15) = 11(10)^2 + 6(10)(15) - 5(15)^2 = 1100 + 900 - 1125 = $875. 
Now, to find the marginal profit of increasing the sales of model A from 10 to 11 units while holding the sales of model B at 15 units, we need to find 
P(11,15) - P(10,15) = [11(11)^2 + 6(11)(15) - 5(15)^2] - [11(10)^2 + 6(10)(15) - 5(15)^2] 
= 1331 + 990 - 1125 - 1100 - 900 + 1125 = $321. 
Therefore, the interpretation of Px(10,15) is that the profit earned when 10 units of model A and 15 units of model B are sold is $875, and increasing the sales of model A by one unit while holding the sales of model B at 15 units will increase the profit by approximately $321. This matches with option B, which states that increasing sales of model A by one unit and holding sales of model B at 15 units will increase profit by approximately $80.

Solve the Problem. -The Profit Function for Sales of Two Models of Television