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The figure shows graphs of the marginal revenue function R' and the marginal cost function C" for a manufacturer. [Recall from Section 4.7 that R (x) and C (x) represent the revenue and cost when * units are manufactured. Assume that R and Care measured in thousands of dollars.] What is the meaning of the area of the shaded region? Use the Midpoint Rule to estimate the value of this quantity.

The figure shows graphs of the marginal revenue function R' and the marginal cost function C" for a manufacturer. [Recall from Section 4.7 that R (x) and C (x) represent the revenue and cost when * units are manufactured. Assume that R and Care measured in thousands of dollars.] What is the meaning of the area of the shaded region? Use the Midpoint Rule to estimate the value of this quantity.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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I need help on this question? Midpoint estimation isn't needed

The figure shows graphs of the marginal revenue function \( R'(x) \) and the marginal cost function \( C'(x) \) for a manufacturer. [Recall from Section 4.7 that \( R(x) \) and \( C(x) \) represent the revenue and cost when \( x \) units are manufactured. Assume that \( R \) and \( C \) are measured in thousands of dollars.] What is the meaning of the area of the shaded region? Use the Midpoint Rule to estimate the value of this quantity. The accompanying graph has the following features: - The x-axis represents the number of units \( x \). - The y-axis represents the value of the marginal functions \( R'(x) \) and \( C'(x) \), measured in thousands of dollars. - The graph displays two curves: - \( R'(x) \) is a downward-sloping line starting at approximately 4 on the y-axis and declining to intersect the x-axis around \( x = 100 \). - \( C'(x) \) is a concave up curve starting just above 1 on the y-axis and increasing to intersect \( R'(x) \). - There is a shaded region between \( R'(x) \) and \( C'(x) \) beginning near \( x = 0 \) and ending around their intersection. The shaded area represents the difference between marginal revenue and marginal cost over the given interval, which can be interpreted as the additional profit or loss from producing those units. To estimate the value of the shaded region using the Midpoint Rule, you would calculate the average height of the difference between \( R'(x) \) and \( C'(x) \) at several midpoints and multiply by the width of the intervals chosen.
Transcribed Image Text:The figure shows graphs of the marginal revenue function \( R'(x) \) and the marginal cost function \( C'(x) \) for a manufacturer. [Recall from Section 4.7 that \( R(x) \) and \( C(x) \) represent the revenue and cost when \( x \) units are manufactured. Assume that \( R \) and \( C \) are measured in thousands of dollars.] What is the meaning of the area of the shaded region? Use the Midpoint Rule to estimate the value of this quantity. The accompanying graph has the following features: - The x-axis represents the number of units \( x \). - The y-axis represents the value of the marginal functions \( R'(x) \) and \( C'(x) \), measured in thousands of dollars. - The graph displays two curves: - \( R'(x) \) is a downward-sloping line starting at approximately 4 on the y-axis and declining to intersect the x-axis around \( x = 100 \). - \( C'(x) \) is a concave up curve starting just above 1 on the y-axis and increasing to intersect \( R'(x) \). - There is a shaded region between \( R'(x) \) and \( C'(x) \) beginning near \( x = 0 \) and ending around their intersection. The shaded area represents the difference between marginal revenue and marginal cost over the given interval, which can be interpreted as the additional profit or loss from producing those units. To estimate the value of the shaded region using the Midpoint Rule, you would calculate the average height of the difference between \( R'(x) \) and \( C'(x) \) at several midpoints and multiply by the width of the intervals chosen.
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