Answer:
a. R(x) = 48.5x - x5inx
b. R'(x) = 43.5 - 5lnx
c. The correct option is d. Yes, because the revenue will be maximized when R'(x)=0. The price to the consumer would be $5.
Explanation:
Given:
p(x) = 48.5 - 5lnx, for 0 ≤ x ≤ 800 ............. (1)
a. Find R(x).
R (x) = x * p (x) ........................ (2)
Substitute equation (1) into (2), we have:
R(x) = x(48.5 - 5lnx)
R(x) = 48.5x - x5inx .............................. (3)
Equation (1) is the R(x) required to be found.
b. Find the marginal revenue, R'(x)
The derivative of equation (3) is taken to obtain R'(x) as follows:
R'(x) = 48.5 - 5lnx - x5(1/x)
R'(x) = 48.5 - 5lnx - 5
R'(x) = 48.5 - 5 - 5lnx
R'(x) = 43.5 - 5lnx ...................... (4)
Equation (4) is the marginal revenue, R'(x), required to found.
c. Is there any price at which revenue will be maximized? Why or why not? Choose the correct answer below.
Profit is maximized when R'(x) = 0
Equating equation (4) to 0 and solve for x, we have:
43.5 - 5lnx = 0
43.5 = 5lnx
5lnx = 43.5
lnx = 43.5 / 5
x = e^(43.5 / 5)
x = 6,002.91
Substituting x = 6,002.91 into equation (1), we have:
p(x) = 48.5 - (5 * ln(6,002.91))
p(x) = 48.5 - (5 * 8.70)
p(x) = 48.5 - 43.5
p(x) = $5
Therefore, the correct option is d. Yes, because the revenue will be maximized when R'(x)=0. The price to the consumer would be $5.
Mill Company began operations on January 1, 20X1, and recognized income from construction-type contracts under different methods for tax purposes and financial reporting purposes. Information concerning income recognition under each method is as follows: Year Tax Purposes Book Purposes 20X1 $ 400,000 $ 0 20X2 625,000 375,000 20X3 750,000 850,000 Required: Assume the income tax rate is 21% in all years and that Mill has no other temporary differences. In its December 31, 20X3, balance sheet, what amount of deferred income taxes should Mill report
Answer:
Deferred tax asset balance on December 31, 20X3 = $115,500
Explanation:
The computation of the amount of deferred income taxes should Mill report is shown below:
Year Tax purpose Book purpose Difference Deferred tax book
20X1 $400,000 $0 $400,000 $84,000
20X2 $625,000 $375,000 $250,000 $52,500
20X3 $750,000 $850,000 ($100,000) ($21,000)
Deferred tax asset balance on December 31, 20X3 = $115,500