Matched Problem 3 Repeat Example 3 with P ( x , y ) = − 66 x 2 + 132 x y − 99 y 2 + 132 x – 66 y – 19 EXAMPLE 3 Profit Suppose that the surfboard company discussed earlier has developed the yearly profit equation P ( x , y ) = − 22 x 2 + 22 x y − 11 y 2 + 110 x − 44 y − 23 where x is the number (in thousands) of standard surfboards produced per year, y is the number (in thousands) of competition surfboards produced per year, and P is profit (in thousands of dollars). How many of each type of board should be produced per year to realize a maximum profit? What is the maximum profit?
Matched Problem 3 Repeat Example 3 with P ( x , y ) = − 66 x 2 + 132 x y − 99 y 2 + 132 x – 66 y – 19 EXAMPLE 3 Profit Suppose that the surfboard company discussed earlier has developed the yearly profit equation P ( x , y ) = − 22 x 2 + 22 x y − 11 y 2 + 110 x − 44 y − 23 where x is the number (in thousands) of standard surfboards produced per year, y is the number (in thousands) of competition surfboards produced per year, and P is profit (in thousands of dollars). How many of each type of board should be produced per year to realize a maximum profit? What is the maximum profit?
Solution Summary: The author calculates the profit function P(x,y) for the number of standard surfboards produced per year.
P
(
x
,
y
)
=
−
66
x
2
+
132
x
y
−
99
y
2
+
132
x
–
66
y
–
19
EXAMPLE 3 Profit Suppose that the surfboard company discussed earlier has developed the yearly profit equation
P
(
x
,
y
)
=
−
22
x
2
+
22
x
y
−
11
y
2
+
110
x
−
44
y
−
23
where x is the number (in thousands) of standard surfboards produced per year, y is the number (in thousands) of competition surfboards produced per year, and P is profit (in thousands of dollars). How many of each type of board should be produced per year to realize a maximum profit? What is the maximum profit?
Suppose P(x) represents the profit on the sale of x Blu-ray discs. If P(1,000) = 2,000 and P'(1,000) = -3, what do these
values tell you about the profit?
%3D
%3D
P(1,000) represents the profit on the sale of
Blu-ray discs. P(1,000) = 2,000, so the profit on
%3D
the sale of
Blu-ray discs is $
. P'(x) represents the
---Select----
O as a function of x. P'(1,000) = -3, so the profit is decreasing at the rate of
per additional Blu-ray disc sold.
%24
Chapter 7 Solutions
Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.
01 - What Is A Differential Equation in Calculus? Learn to Solve Ordinary Differential Equations.; Author: Math and Science;https://www.youtube.com/watch?v=K80YEHQpx9g;License: Standard YouTube License, CC-BY
Higher Order Differential Equation with constant coefficient (GATE) (Part 1) l GATE 2018; Author: GATE Lectures by Dishank;https://www.youtube.com/watch?v=ODxP7BbqAjA;License: Standard YouTube License, CC-BY