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iren2701 [21]
2 years ago
9

The quantity demanded x for a product is inversely proportional to the cube of the price p for p > 1. When the price is $10 p

er unit, the quantity demanded is 64 units. The initial cost is $140 and the cost per unit is $4. What price will yield a maximum profit? (Round your answer to two decimal places.)
$______
Business
1 answer:
Delvig [45]2 years ago
4 0

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

                                             

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Jan 01, 2021    Patent Rights (Debit)                    210,000

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Requirement 3. Journal for amortization expense for the year ended 31 Dec, 2022:

Dec 31, 2022    Amortization expense - Patent    35,000

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Requirement 1.

Since Weaver corporation purchases a patent, it costs the company cash or bank balance. As the patent is a non-current intangible asset, it is a debit. On the other hand, as cash decreases due to the purchase of patent, the cash is a credit. In this journal, an asset (Non-current asset) increases, and another asset (Current asset) decreases. There will be no effect on the total asset.

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