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Answer:
$6.00
Explanation:
Given data
quantity demanded ( x ) ∝ 1 / p^3 for p > 1
when p = $10/unit , x = 64
initial cost = $140, cost per unit = $4
<u>Determine the price that will yield a maximum profit </u>
x = k/p^3 ----- ( 1 ). when x = 64 , p = $10 , k = constant
64 = k/10^3
k = 64 * ( 10^3 )
= 64000
back to equation 1
x = 64000 / p^3
∴ p = 40 / ∛x
next calculate the value of revenue generated
Revenue(Rx) = P(price ) * x ( quantity )
= 40 / ∛x * x = 40 x^2/3
next calculate Total cost of product
C(x) = 140 + 4x
Maximum Profit generated = R(x) - C(x) = 0
= 40x^2/3 - 140 + 4x = 0
= 40(2/3) x^(2/3 -1) - 0 - 4 = 0
∴ ∛x = 20/3 ∴ x = (20/3 ) ^3 = 296
profit is maximum at x(quantity demanded ) = 296 units
hence the price that will yield a maximum profit
P = 40 / ∛x
= ( 40 / (20/3) ) = $6
Answer:
- <u><em>Option B. $1,025 a month for 10 years.</em></u>
Explanation:
Calculate the present value of each option:

Formula:
![PV=C\times \bigg[\dfrac{1}{r}-\dfrac{1}{r(1+r)^t}\bigg]](https://tex.z-dn.net/?f=PV%3DC%5Ctimes%20%5Cbigg%5B%5Cdfrac%7B1%7D%7Br%7D-%5Cdfrac%7B1%7D%7Br%281%2Br%29%5Et%7D%5Cbigg%5D)
Where:
- PV is the present value of the constant monthly payments
- r is the monthly rate
- t is the number of moths
<u>1. Option A will provide $1,500 a month for 6 years. </u>
![PV=$\ 1,500\times \bigg[\dfrac{1}{(0.005\overline 6}-\dfrac{1}{0.005\overline 6(1+0.005\overline 6)^{(6\times12)}}\bigg]](https://tex.z-dn.net/?f=PV%3D%24%5C%201%2C500%5Ctimes%20%5Cbigg%5B%5Cdfrac%7B1%7D%7B%280.005%5Coverline%206%7D-%5Cdfrac%7B1%7D%7B0.005%5Coverline%206%281%2B0.005%5Coverline%206%29%5E%7B%286%5Ctimes12%29%7D%7D%5Cbigg%5D)

<u>2. Option B will pay $1,025 a month for 10 years. </u>
![PV=$\ 1,025\times \bigg[\dfrac{1}{(0.005\overline 6}-\dfrac{1}{0.005\overline 6(1+0.005\overline 6)^{(10\times12)}}\bigg]](https://tex.z-dn.net/?f=PV%3D%24%5C%201%2C025%5Ctimes%20%5Cbigg%5B%5Cdfrac%7B1%7D%7B%280.005%5Coverline%206%7D-%5Cdfrac%7B1%7D%7B0.005%5Coverline%206%281%2B0.005%5Coverline%206%29%5E%7B%2810%5Ctimes12%29%7D%7D%5Cbigg%5D)

<u>3. Option C offers $85,000 as a lump sum payment today. </u>
<u></u>
<h2 /><h2> Conclusion:</h2>
The present value of the<em> option B, $1,025 a month for 10 years</em>, has a the greatest present value, thus since he is only concerned with the <em>financial aspects of the offier</em>, this is the one he should select.
I am pretty sure that the answer is the money market account
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Hope this helps