Answer:
A) R(x) = 120x - 0.5x^2
B) P(x) = - 0.75x^2 + 120x - 2500
C) 80
D) 2300
E) 80
Explanation:
Given the following :
Price of suit 'x' :
p = 120 - 0.5x
Cost of producing 'x' suits :
C(x)=2500 + 0.25 x^2
A) calculate total revenue 'R(x)'
Total Revenue = price × total quantity sold, If total quantity sold = 'x'
R(x) = (120 - 0.5x) * x
R(x) = 120x - 0.5x^2
B) Total profit, 'p(x)'
Profit = Total revenue - Cost of production
P(x) = R(x) - C(x)
P(x) = (120x - 0.5x^2) - (2500 + 0.25x^2)
P(x) = 120x - 0.5x^2 - 2500 - 0.25x^2
P(x) = - 0.5x^2 - 0.25x^2 + 120x - 2500
P(x) = - 0.75x^2 + 120x - 2500
C) To maximize profit
Find the marginal profit 'p' (x)'
First derivative of p(x)
d/dx (p(x)) = - 2(0.75)x + 120
P'(x) = - 1.5x + 120
-1.5x + 120 = 0
-1.5x = - 120
x = 120 / 1.5
x = 80
D) maximum profit
P(x) = - 0.75x^2 + 120x - 2500
P(80) = - 0.75(80)^2 + 120(80) - 2500
= -0.75(6400) + 9600 - 2500
= -4800 + 9600 - 2500
= 2300
E) price per suit in other to maximize profit
P = 120 - 0.5x
P = 120 - 0.5(80)
P = 120 - 40
P = $80
Answer:
If the company process further the units, income will decrease by $600.
Explanation:
Giving the following information:
A company has a process that results in 1,300 pounds of Product A that can be sold for $13.00 per pound.
An alternative would be to process Product A further for $13,600 and then sell it for $23.00 per pound.
We need to determine the result of further processing the product.
Sell as-is:
Effect on income= 1,300*13= $16,900 increase
Continue processing:
Effect on income= 1,300*23 - 13,600= $16,300
It is more profitable to sell the units before further processing.
Answer: The labor efficiency variance for the month is closest to: $2576
Explanation:
Given:
Actual output 8,800 units
Actual direct labor-hours 1,610 hours
Actual direct labor rate $ 23.30 per hour
The labor efficiency variance for the month is computed as :
The labor rate variance = Actual hours×(Actual rate - Standard rate)
=1610 ×($23.30-$21.70)
=$2576
Answer:
c. The capital gain would be automatically re-invested at NAV if not taken in cash while the purchase of the shares would occur at POP including a sales charge.
Explanation:
An Asset appreciation doesn't in any way complete a breakpoint for a client. The client agreed to buy $50,000 of fund shares under a Letter of Intent to get a lower sales charge. If the customer doesn't deposit the full $50,000, then the sales charge is calculated to a higher percentage, which is based on the customer's purchase. The customer must deposit another $10,000 to complete the breakpoint.
If the customer were to take the capital gains distribution as cash and use that money to buy additional shares to complete the breakpoint, the customer would then have to pay a sales charge, which would be lower because the breakpoint is being completed. The customer must know that if the capital gains distribution were reinvested, it would occur at NAV and there would be no sales charge increase in sales charge. Whether the capital gain is taken as cash or it is reinvested, it is taxable.
