The profit function is given by:
P(q) = pq - C(q) = (64-2q)q - (90+16q) = -2q^2 + 32q - 90
To find the number of units that produces maximum profit, we need to find the vertex of the parabola. The vertex occurs at:
q = -b/2a = -32/(-4) = 8
Therefore, the optimum number of units is 8.
To find the price per unit that produces maximum profit, we substitute q=8 into the price function:
p = 64 - 2q = 64 - 16 = 48
Therefore, the optimum price per unit is 48.
Finally, to find the maximum profit, we substitute q=8 and p=48 into the profit function:
P = pq - C(q) = (48)(8) - (90+16(8)) = $114
Therefore, the maximum profit is $114.
For the cost and price functions below, find the number, q, of units that produces maximum profit; the price, p, per unit that produces maximum profit; and the maximum profit, P.
C(q)=90+16q; p=64-2q
3 answers
An accountant for a corporation forgot to pay the firm's income tax of $725,933.62 on time. The government charged a penalty of 8.3% interest for the 55 days the money was late. Find the total amount (tax and penalty) that was paid. Assume 365 days in a year.
First, we need to find the amount of penalty charged:
Penalty = Tax amount x Rate x Time
Penalty = 725,933.62 x 0.083 x (55/365)
Penalty = 9,627.28
The penalty charged was $9,627.28.
To find the total amount (tax and penalty) paid, we add the penalty to the original tax amount:
Total amount = Tax amount + Penalty
Total amount = 725,933.62 + 9,627.28
Total amount = $735,560.90
Therefore, the total amount (tax and penalty) that was paid was $735,560.90.
Penalty = Tax amount x Rate x Time
Penalty = 725,933.62 x 0.083 x (55/365)
Penalty = 9,627.28
The penalty charged was $9,627.28.
To find the total amount (tax and penalty) paid, we add the penalty to the original tax amount:
Total amount = Tax amount + Penalty
Total amount = 725,933.62 + 9,627.28
Total amount = $735,560.90
Therefore, the total amount (tax and penalty) that was paid was $735,560.90.
1 answer