Round the answers to 2 decimal places. Travis Scott spent x thousands of dollars on advertising and promoting for his Astroworld tour. Assume that R(x) = 50, 805 – 5x3 + 80x2 +55x, where 0

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Chapter1: Making Economics Decisions
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I only got so far with this question before I gave up trying to solve it on my own when I was about 60 minutes into it and I still wasn't getting anywhere. I'm completely lost on this question if someone could please help guide me through on how to complete it I would really appreciate the help.

Round the answers to 2 decimal places. Travis Scott spent x thousands of dollars on advertising and
promoting for his Astroworld tour. Assume that R(x) = 50, 805 – 5.x³ + 80x2 + 55x, where 0 < x < 17.
(a)
Find the maximum revenue.
(b)
Find the potential point of diminishing returns and confirm that it is indeed the
point of diminishing returns by checking concavity.
Transcribed Image Text:Round the answers to 2 decimal places. Travis Scott spent x thousands of dollars on advertising and promoting for his Astroworld tour. Assume that R(x) = 50, 805 – 5.x³ + 80x2 + 55x, where 0 < x < 17. (a) Find the maximum revenue. (b) Find the potential point of diminishing returns and confirm that it is indeed the point of diminishing returns by checking concavity.
Expert Solution
Step 159

a)

To find the maximum revenue, we need to find first-order differentiation, set it equal to 0 to get the x which will maximize the revenue and then put the value of x in a revenue function.

R(x) = 50,805 - 5x3+80x2+55xR'=dR(x)dx= -15x2+160x+55 = 0

To solve the quadratic equation, use the quadratic formula by comparing the quadratic equation with ax2+bx+c=0.

So, a = -15, b= 160, and c = 55

x1,x2=-b±b2-4ac2ax1,x2=-160±1602-4-15552-15x1,x2=-13, 11

Since x cannot be negative so x=  11.

So the maximum revenue will be,

R(11) = 50,805 - 5113+80112+5511R(11) = 50,805 - 6,655+9,680+605R(11) =54,435

 

 

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