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s.h_math s.h_math
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A year ago
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I tried subbing in the values but it only works for the first row not really sure why

Suppose your total benefits of renting x DVD's next month is:
— + 16x+ 50
The cost of renting a DVD is $2, and so the total cost of renting x DVD's is $2x.
Calculate your net benefit from watching 1, 2...8 DVDs. Complete column (2). (Enter your responses as integers.)
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wrote...
#1
Educator
A year ago


s.h_math Author
wrote...
#2
A year ago
It said one or more of your responses is incorrect. The total net benefit is the total benefit minus the total cost. The total benefit is
-X + 16x + 50, where x is DVDs watched. The total cost is $2x.
wrote...
#3
Educator
A year ago
Net benefit = Total benefit \(-\) total cost.

Total benefit of renting \(x\) DVD's next month is \(-x^2+16x+50\)

Total cost renting x DVD's is $\(2x\)

Thus: \(-x^2+16x+50-2x\rightarrow -x^2+14x+50\)

\(-\left(1\right)^2+14\left(1\right)+50=63\)

\(-\left(2\right)^2+14\left(2\right)+50=74\)

3) 83

4) 90

5) 95

6) 98

7) 99

8) 98
s.h_math Author
wrote...
#4
A year ago
Now they ask this does that mean I would substitute 7 in the equation?
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wrote...
#5
Educator
A year ago Edited: A year ago, bio_man
As per the principle of optimization at the margin, the optimal DVDs to rent is where marginal cost is equal to marginal benefit, therefore, 7 DVDs must be rented where both marginal cost and marginal benefit is 2.

-2x+16 = -2(7)+16 = 2.

Thus, this occurs when x = 7
s.h_math Author
wrote...
#6
A year ago
How do I know that MB=MC at 7?
wrote...
#7
Educator
A year ago
Try all others, from 1 to 8. Only when x=7 is the output 2.
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