In 2016, the city of Vancouver collected $500,000 in taxes and spent $450,000. In 2016, the city of Vancouver had a
1 answer:
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Answer:
The level of production x that will maximize the profit is: 22,966
Explanation:
C(x) = 50,000 + 100x + x³
R(x) = 3400x
P(x) = R(x) - C(x)
= 3400x - [50,000 + 100x + x³]
= 3400x - 50,000 - 100x - x³
= 3300x - 50,000 - x³ .................... (A)
P'(x) = 3300(1) - 0 - 3x²
= 3300 - 3x²
At a critical point, P'(x) = 0
∴ 0 = 3300 - 3x²
3x² = 3300
x² = 1100
x = ±
P"(x) = -6x
P() = -6 (
) < 0
by second derivative, 'P' max at x = = 33.17 (rounds)
since x = ,
recall that P(x) = 3300x - 50,000 - x³ from equation (A)
Therefore, Maximum Profit
P() = 3300
- 50000 -
= 3300(33.17) - 50,000 - 33.17³
= 109461 -50,000 - 36495.26
= 22,965.74
Maximum profit is 22,966 to the nearest whole number
Answer:
2.96% will be effective rate of the investment
Explanation:
First year:
1,000 x 1 + 10%) = 1,100
<em><u>Second year: </u></em>
1,100 + 3,000 = 4,100 invesmtent balance
4,100 x (1 - 5%) = 3,895
<em><u>Third year:</u></em>
3,895 + 2,000 = 5,895
5,895 x (1 + 2%) = 6012.9
<em><u>Fourth year:</u></em>
6012.9 + 500 = 6512.9
6,512.9 x (1+ 8%) = 7033.932
We calcualte rate that is equivalent with the following cash flow:
We solve using excel goal seek
0.029646151