Question

The graphs of the revenue and cost functions for the production and sale of x units are shown below. The cost function is the straight line, and the revenue function is the curve. 15000 14000 13000 12000 11000 10000 9000 8000 7000 6000 5000 4000 3000 2000 1000 50 100 150 200 250 300 350 400 450 500 a. Use the graph to estimate the production level x that maximizes profit. Use only values that appear on the horizontal axis for your estimation. x = units b. What are the points (x, C(x)) and (x, R(x)) on the graphs of the cost and revenue functions corresponding to the value of x that maximizes profit? (x, C(x)) = (x, R(x)) = c. What is the maximum profit? $ d. If the cost per unit decreases, should the production level be raised or lowered to maximize profit? Select an answer

          The graphs of the revenue and cost functions for the production and sale of x units are shown below. The cost function is the straight line, and the revenue function is the curve.

15000
14000
13000
12000
11000
10000
9000
8000
7000
6000
5000
4000
3000
2000
1000
50 100 150 200 250 300 350 400 450 500

a. Use the graph to estimate the production level x that maximizes profit. Use only values that appear on the horizontal axis for your estimation.
x = units

b. What are the points (x, C(x)) and (x, R(x)) on the graphs of the cost and revenue functions corresponding to the value of x that maximizes profit?
(x, C(x)) =
(x, R(x)) =

c. What is the maximum profit? $

d. If the cost per unit decreases, should the production level be raised or lowered to maximize profit?
Select an answer

Show more…

The graphs of the revenue and cost functions for the production and sale of x units are shown below. The cost function is the straight line, and the revenue function is the curve.

15000
14000
13000
12000
11000
10000
9000
8000
7000
6000
5000
4000
3000
2000
1000
50 100 150 200 250 300 350 400 450 500

a. Use the graph to estimate the production level x that maximizes profit. Use only values that appear on the horizontal axis for your estimation.
x = units

b. What are the points (x, C(x)) and (x, R(x)) on the graphs of the cost and revenue functions corresponding to the value of x that maximizes profit?
(x, C(x)) =
(x, R(x)) =

c. What is the maximum profit? d. If the cost per unit decreases, should the production level be raised or lowered to maximize profit?
Select an answer

Added by Connie M.

Calculus: Early Transcendentals

James Stewart 8th Edition

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04/27/2023

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To maximize profit, we need to find the point where the difference between the revenue function (R(€)) and the cost function (C(€)) is the largest. Show more…

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The graphs of the revenue and cost functions for the production and sale of x units are shown below. The cost function is the straight line, and the revenue function is the curve. a. Use the graph to estimate the production level x that maximizes profit. Use only values that appear on the horizontal axis for your estimation. x = units b. What are the points (x, C(x)) and (x, R(x)) on the graphs of the cost and revenue functions corresponding to the value of x that maximizes profit? (x, C(x)) = (x, R(x)) = c. What is the maximum profit? $ d. If the cost per unit decreases, should the production level be raised or lowered to maximize profit? Select an answer

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00:01 The revenue and cost functions for the production and sale of x units are shown in the graph.

00:04 The cost function is linear and the revenue function is the curve.

00:08 We want to use the graph to estimate the production level x that will maximize the profit.

00:12 So, our profit will be the revenue function minus the cost function.

00:21 So, to maximize that profit we want this difference r and c to be as large as possible.

00:28 We want r minus c maximized.

00:33 So, what does r minus c look like graphically? we have the revenue function here, r of x, and the cost function is the linear c of x.

00:46 The difference between those is just the vertical distance between the graphs in between.

00:53 So like at 100 that's the difference right here.

00:58 At 150 that's the difference.

00:59 At 200 there's the difference.

01:02 Let's get a different color to see those differences better.

01:05 So we can see those differences or those heights are different lengths.

01:10 So, we want that difference to be maximized.

01:13 So, we just need to figure out which of these differences is the biggest.

01:17 We can see at 200 that's where that line will be the biggest.

01:21 So, just estimating at x equals 200 the profit will be maximized because that's the greatest difference between the revenue and the cost where the revenue is greater than the cost.

01:34 Okay, now we want to find the points x, c of x, and r of x on the graph for the function that correspond to the value of x that maximize the profit.

01:45 So, for the cost curve, the cost line, that will be the point.

01:53 We're using this point right here.

01:55 That's the point when x is 200 and the cost at that time looks to be 9 ,000...

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