A company provides the following data for material costs: Standard cost per unit 3 pounds at $2 per unit Actual cost per unit 2.
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:
The fed needs to purchase bonds worth $20 from the banks to increase money supply by $200.
Explanation:
The Federal Reserve wants to increase the money supply by $200.
The reserve requirement is 10%.
The fed can increase the money supply by purchasing bonds from commercial banks.
The money supply will increase by money multiplier times worth of bonds.
Increase in money supply =
$200 =
Worth of bonds =
Worth of bonds = $20
So the fed needs to purchase bonds worth $20 from the banks to increase money supply by $200.