The monthly profit for a small company that makes long-sleeve T-shirts depends on the price per shirt, If the price is too high, sales will drop. If the price is too low, the revenue brought in may not cover the cost to produce the shirts. After months of data collection, the sales team determines that the monthly profit is approximated by f p = − 50 p 2 + 1700 p − 12 , 000 , where p is the price per shirt and f p is the monthly profit based on that price. (See Example 4) a. Find the price that generates the maximum profit. b. Find the maximum profit. c. Find the price(s) that would enable the company to break even.
The monthly profit for a small company that makes long-sleeve T-shirts depends on the price per shirt, If the price is too high, sales will drop. If the price is too low, the revenue brought in may not cover the cost to produce the shirts. After months of data collection, the sales team determines that the monthly profit is approximated by f p = − 50 p 2 + 1700 p − 12 , 000 , where p is the price per shirt and f p is the monthly profit based on that price. (See Example 4) a. Find the price that generates the maximum profit. b. Find the maximum profit. c. Find the price(s) that would enable the company to break even.
The monthly profit for a small company that makes long-sleeve T-shirts depends on the price per shirt, If the price is too high, sales will drop. If the price is too low, the revenue brought in may not cover the cost to produce the shirts. After months of data collection, the sales team determines that the monthly profit is approximated by
f
p
=
−
50
p
2
+
1700
p
−
12
,
000
,
where p is the price per shirt and
f
p
is the monthly profit based on that price. (See Example 4)
a. Find the price that generates the maximum profit.
b. Find the maximum profit.
c. Find the price(s) that would enable the company to break even.
1. A bicyclist is riding their bike along the Chicago Lakefront Trail. The velocity (in
feet per second) of the bicyclist is recorded below. Use (a) Simpson's Rule, and (b)
the Trapezoidal Rule to estimate the total distance the bicyclist traveled during the
8-second period.
t
0 2
4 6 8
V
10 15
12 10 16
2. Find the midpoint rule approximation for
(a) n = 4
+5
x²dx using n subintervals.
1° 2
(b) n = 8
36
32
28
36
32
28
24
24
20
20
16
16
12
8-
4
1
2
3
4
5
6
12
8
4
1
2
3
4
5
6
=
5 37
A 4 8 0.5
06
9
Consider the following system of equations, Ax=b :
x+2y+3z - w = 2
2x4z2w = 3
-x+6y+17z7w = 0
-9x-2y+13z7w = -14
a. Find the solution to the system. Write it as a parametric equation. You can use a
computer to do the row reduction.
b. What is a geometric description of the solution? Explain how you know.
c. Write the solution in vector form?
d. What is the solution to the homogeneous system, Ax=0?
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
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