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il63 [147K]
3 years ago
10

What is a lifetime cap?

Mathematics
1 answer:
Nostrana [21]3 years ago
5 0
A lifetime cap is the maximum interest rate a borrower could ever pay during the life of a loan.
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A concession stand at a sports stadium sells 600 bags of peanuts (each game) if the price of each bag is $4.00. For each $0.25 i
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Price = $4.50

Maximum revenue = $2,430

Step-by-step explanation:

The concession stand sells 600 bags of peanut at $4.00 (600, $4.00).

If there is a $1 increase in price, the number of bags old will decrease by 120, which mens that 480 bags of peanuts will be sold at $5.00 (480, $5.00).

Tracing a linear relationship between price and quantity sold with the two given points:

m = \frac{5-4}{480-600}\\ m=-\frac{1}{120}

P - P_0=m*(Q-Q_0)\\P-4.00=-\frac{1}{120} (Q-600)\\P= -\frac{1}{120}Q +9

The revenue function is given by the price multiplied by the quantity sold:

R=Q*P= (-\frac{1}{120}Q +9)*Q\\R=-\frac{1}{120}Q^2 +9Q

The value of 'Q' for which the derivate of the revenue function is zero, is the output level for which revenue is maximum:

R'=0=-\frac{2}{120}Q+9\\Q_{max} = 540\\P_{max} = -\frac{540}{120} +9\\P_{max} =\$4.50

The total revenue of 540 units at $4.50 per unit is:

R = \$4.50*540\\R=\$2,430

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3 years ago
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