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Marizza181 [45]
3 years ago
14

The demand function for our product is: Q=90-0.1P^2

Mathematics
1 answer:
melisa1 [442]3 years ago
3 0
Assuming that "elasticity" = P:

A. Q=90-0.1P^2\\50=90-0.1P^2\\-40=-0.1P^2\\400=P^2\\20=P\\\\\frac{dQ}{dP}=-0.2P\\E=\frac{P}{Q}*\frac{dQ}{dP}\\E=\frac{(20)}{(90)}(-0.2P)\\E=\frac{-2(20)}{45}\\E=\frac{-8}{9} - Elasticity = -0.889

B. 0>\frac{-8}{9}>-1>-\infty - The demand is inelastic because the elasticity > -1.

(C). Set P and Q to 1 in two separate functions. If Q < P revenue will increase. If Q > P revenue will decrease.

Q=90-0.1P^2\\Q=90-0.1(1)^2\\Q=90-0.1\\Q=89.9\\\\(1)=90-0.1P^2\\-89=-0.1P^2\\890=P^2\\\sqrt{890}=P\\P=29.833\\Q>P\\(89.9)>(29.833)

Q > P therefore revenue will decrease.

(D). Q=90-0.1P^2\\\frac{dQ}{dP}=-0.2P\\-0.2P=0\\P=0

One obviously won't be able to maximize revenue if their price per unit, <em>P</em>, equals 0. Quantity of a product can only be sold in whole, so the closest integer to 90 is 89. The value of P that maximizes revenue is Q=90-0.1P^2\\(89)=90-0.1P^2\\-1=-0.1P^2\\10=P^2\\\sqrt{10}=P - sqrt(10).

Therefore, the values of P and Q that maximize revenue are 3.162 and 89, respectively.
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You go to a local mechanic to get your tires changed. The tires cost $300. There is a 6% sales tax, but you get a 10% discount.
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Answer:

a) T(x)=300x+18x=318x

b) D(x)=318x-(0.1)(318)+10x\\=296.2x

c) Yes.

Step-by-step explanation:

We have that:

Tires=$300\\Tax=0.006\\Discount=0.1\\

And we have $10 free of taxes.

Making x= number of tires to buy, then we have that the total cost of tires is:

Total_{Tires}=300x

So, what we pay for taxes is given by:

Taxes=(300x)(0.06)=18x

a) Then, according to the above, we can write down the total cost before the discount as:

T(x)=300x+18x=318x

b) And the total cost after discounts, is then given by:

D(x)=318x-(0.1)(318)+10x\\=296.2x

c) If the discount is added first, then less tax will be paid because the amount on which it is paid is lower. If the discount is added later, then the taxes will have been taxed on a higher amount, so it does matter whether they are added first or later.

6 0
3 years ago
Tomas is making trail mix using granola and walnuts. He can spend a total of $12 on the ingredients. He buys 3 pounds of
spin [16.1K]

Answer:

The first error that Tomas made was added 6 to both sides of the equation instead of subtracting 6

Step-by-step explanation:

Let

x ----> represents the number of pounds of granola

y ----> represents the number of pounds of walnuts

we know that

The linear equation that represent this scenario is

2x+6y=12 -----> equation A

x=3 -----> equation B

substitute equation B in equation A and solve for y

2(3)+6y=12

6+6y=12

Subtract 6 both sides

6+6y-6=12-6

6y=6

Divide by 6 both sides

6y/6=6/6

y=1

so

The number of pounds of walnuts is 1

therefore

The first error that Tomas made was added 6 to both sides of the equation instead of subtracting 6

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Answer:

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Step-by-step explanation:

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a famer has 120 feet of fencing with whcih to enclose two adjacent rectangular pens as shown. what dimeensions should be used th
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The dimensions of the rectangular pen should be 15 by 20 feet and the maximum area is 1200 square feet.

Let the area be y .

Area = (base) × (height)

Base = 2x

Height = h

Let the area of the rectangular pens be y .

∴ y = 2xh

Perimeter of all the fencing = 4x+3h

∴ 4x+3h = 120

now we solve for h

3h = 120-4x

h = 40 - 4/3 x

Now we will substitute this value in the above first equation:

y = 2xh

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or, y = 80x - 8/3 x²

Now for the maximum area we have to find the first order differentiation of y

now,

dy /dx = 80 - 16/3 x

At dy/dx = 0 we get the value of x for which y is maximum.

80 - 16/3 x = 0

or, - 16/3 x = -80

or, x = 15 feet

Hence height =  40 - 4/3 x = 40 - 20 = 20feet

Maximum area = 2xh = 2×15×40 = 1200 square feet

The dimensions of the rectangular pen should be 15 by 20 feet and the maximum area is 1200 square feet.

Disclaimer : The missing figure for the question is attached below.

To learn more about area visit:

brainly.com/question/27531272

#SPJ4

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