Business, 29.07.2019 19:10 calebnlocke

Acar rental agency rents 220 cars per day at a rate of $30 per day. for each $1 increase in rate, 5 fewer cars are rented. at what rate should the cars be rented to produce the maximum income? what is the maximum income?

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Answer from: thanitoast84

The cars should be rented at $37 per day

The maximum income is $ 6845

Explanation:

To solve this problem, a model like this is proposed:

1. If for $ 1 increase in rate 5 fewers cars are rented, then for X monetary units 5X fewe cars are rented.

2. This expressed in rate and cars terms is:

Rate= 30 + x

Cars= ( 220 - 5x)

3. And in the income formula is:

Income=Rate X Cars

But the income formula in function of x monetary units [F(x)] is:

F(x)=(220-5x)(30+x)

$F(x)=6600-150x+220x-5x^{2}$

$F(x)=-5x^{2} +70x+6600$

4. F (x) being a quadratic function, in the form $f(x)=ax^{2} +bx+c$ , with , the vertex (h,k) is determined because is the point of maximum values of the function.

The value of x of the vertex will give us in how many monetary units can be increased the rent.

5. We find the value of h with the following formula:

$h=\frac{-b}{2a}$

$h=\frac{-70}{2(-5)}$

h=7

6. We replace the value of h in rate formula:

Rate= 30+h

Rate= 30 + 7

Rate= 37

And we respond the first question: The cars should be rented at $37 per day

7. We replace the value of h in F(x) or Income formula:

$F(x)=-5x^{2} +70x+6600$

$F(x)=-5(7)^{2} +70(7)+6600$

F(x)=-245 +490+6600

F(x)= 6845

Income= Rate X Cars

Income = 37 X (220 - 5(37))

Income= 37 X 185

Income= 6845

And we respond the second question: The maximum income is $ 6845

Answer from: Quest

The answer is b) market forces

Answer from: Quest

$527.7.if the following was the question $527.7 is the answer.students who are trying to raise funds have an agreement with a local pizza chain. the chain has agreed to sell them pizzas at a discount, which the students can then resell to families in the local community for a profit. it is expected that of the 500 families in the community, at most 70% will buy pizza. based on a survey of their personal preferences, the students believe that they should order no more than 120 cheese pizzas, no more than 150 pepperoni pizzas, and no more than 100 vegetarian pizzas. they also want to make sure that at least 20% of the total pizzas are cheese and at least 50% of the pizzas are pepperoni. they make a profit of $1.45, $1.75, and $1.98, respectively, for each cheese, pepperoni, and vegetarian pizza they resell. how many pizzas of each type should they buy?

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Acar rental agency rents 220 cars per day at a rate of $30 per day. for each $1 increase in rate, 5...