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FinnZ [79.3K]
3 years ago
7

A car rental agency rents 200 cars per day at a rate of 29 dollars per day. For each 1 dollar increase in the daily rate, 5 fewe

r cars are rented. At what rate should the cars be rented to produce the maximum income, and what is the maximum income? R
Business
1 answer:
Irina-Kira [14]3 years ago
3 0

Answer and Explanation:

Given:

Total car = 200

Rate = $29

Computation:

Total increase in rate = a

So , Total decrees in car = 5a

Total income (y) = [200-5a][29+a]

y = 5,800 + 200a - 145a - 5a²

y = 5,800 + 55a - 5a²

y' = dy / da [5,800 + 55a - 5a²]

y' = -10a + 55

in which , y' = 0

0 = -10a + 55

a = 5.5

So , Maximum rate = $ [29+5.5]

Maximum rate = $34.5

maximum income = 5,800 + 55(5.5)- 5(5.5)²

maximum income = 5,800 + 302.5 - 151.25

maximum income = $5951.25

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Explanation:

Calculation to determine How much less than your brother will you have to deposit today

Using this formula

FV= Present value × (1 + interest rate)^number of years

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$28,000 = Present value × (1 + 0.112)^13

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Answer:

Part 1.  inelastic.

Part 2. inelastic.

Part 3. inelastic.

Explanation:

When the coefficient of elasticity of demand is less than 1, demand is inelastic, when it is equal to 1, demand is unitary elastic, when it is greater than 1, demand is elastic, and when it is equal to zero demand is perfectly inelastic.

Part 1

Price Elasticity of demand =  (dQ/dP) x P/Q

  Where : dQ = Change in Quantity

               dP = Change in Price

                 P = Initial or Old price

                 Q = Initial of Old Quantity

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Price Elasticity of demand = (-$5,000/$2) * $8/ $40,000

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Disregard the minus sign,  since elasticity of demand is less than 1, demand is inelastic.

Part 2

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Disregard the minus sign,  since elasticity of demand is less than 1, demand is inelastic.

Part 3

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