Advanced Placement (AP), 08.10.2021 01:00 AquaTyrant5054

A firm produces and sells a product with a contribution margin of $32 per unit. The firm is presently selling 90,000 units and earning $240,000 in after-tax income. Taxes are $80,000 at a 25% tax rate. If the firm desires to increase its after-tax income to $300,000, how many more units must it sell?

Answers: 1

Show answers

Answers

Answer from: hosteenimport21

9514 1404 393

2500 more units

Explanation:

The after-tax contribution margin per unit is ...

$32 - 25%×$32 = $32 -8 = $24

To increase the after-tax income from $240,000 to $300,000, an increase of ...

$300,000 -240,000 = $60,000

is required. If each unit contributes $24 in after-tax income, then the number of additional units required is ...

$60,000/($24/unit) = 2500 units

The firm must sell 2500 more units to make the desired increase in after-tax income.

Answer from: Quest

Extrusive;

Answer from: Quest

Answer: the interval on which the curve is concave up is (-∞, -1/2)====== $\displaystyle y = \int_{0}^x \frac{1}{1 + t + t^2} \; dt$ we find the interval where this curve is concave up by finding the interval in which the 2nd derivative is positive.differentiate the curve equation with respect to x $\begin{aligned} \frac{dy}{dx} & = \frac{d}{dx} \int_{0}^x \frac{1}{1 + t + t^2} \; dt \end{aligned}$ let the function f denote be the anti-derivative of the inside expression, i.e. a function such that $(d/dx)f(x) = 1/(1 + t + t^2)$ .then use the fundamental theorem of calculus: $\begin{aligned} \frac{dy}{dx} & = \frac{d}{dx} \int_{0}^x \frac{1}{1 + t + t^2} \; dt \\& = \frac{d}{dx} \big[ f(x) - f(0) \big] & & \text{\footnotesize apply ftc} \\ & = \frac{d}{dx}f(x) - 0 \\ & = \frac{1}{x + x + x^2} & & \text{\footnotesize since $\frac{d}{dx}f(x) = \frac{1}{1 + x + x^2}$ } \end{aligned}$ differentiate again to get second derivative. we can use chain rule with 1/x as the outside function and 1 + x + x² as the inside function $\begin{aligned} \frac{d}{dx} \left( \frac{dy}{dx} \right) & = \frac{d}{dx}\left(\frac{1}{1 + x + x^2} \right) \\ \frac{d^2y}{dx^2} & = \frac{-1}{\left(1 + x + x^2\right)^2} \cdot \tfrac{d}{dx}(1 + x + x^2) \\ & = \frac{-1}{\left(1 + x + x^2\right)^2} \cdot (1 + 2x) \\ & = \frac{-(1 + 2x)}{\left(1 + x + x^2\right)^2} \end{aligned}$ find critical numbers of the second derivative. these numbers are where the 2nd deriv. is undefined or zero.where the 2nd derivative is zero: set (d²y/dx²) to equal 0 and solve for x $\begin{aligned} 0 & = \frac{-(1 + 2x)}{\left(1 + x + x^2\right)^2} \\ 0 & = -(1+2x) \\ -1 & = 2x \\ x & = -1/2 \end{aligned}$ where the 2nd derivative is undefined: if the denominator is equal to zero, the derivative will be undefeined. attempting to solve the equation 1 + x + x² = 0results in a discriminant of $b^2 - 4ac = 1^2 - 4(1)(1) = -3$ meaning that the equal 1 + x + x² = 0 has no real solutions and therefore will never equal zero.======our only critical number is x = -1/2.this forms two intervals to test the sign for: (-∞, -1/2) and (-1/2, ∞)test values into the 2nd derivative for (-∞, -1/2)if we try x = -1, we get $\begin{aligned} \left.\frac{d^2y}{dx^2}\right|_{x = -1} & = \frac{-(1+2(-1))}{\left(1+(-1)+(-1)^2\right)^2} \\ & = \frac{-(1-2)}{1} \\ & = 1 \end{aligned}$ so the since the 2nd derivative of the curve is positive on the interval (-∞, -1/2), the curve is concave up on (-∞, -1/2)test values into the 2nd derivative for (-1/2, ∞)if we try x = 0, we get $\begin{aligned} \left.\frac{d^2y}{dx^2}\right|_{x = 0} & = \frac{-(1+2(0))}{\left(1+(0)+(0)^2\right)^2} \\ & = \frac{-(1)}{1} \\ & = -1 \end{aligned}$ so the since the 2nd derivative of the curve is positive on the interval (-∞, -1/2), the curve is concave down on (-∞, -1/2).the interval on which the curve is concave up is (-∞, -1/2)

Another question on Advanced Placement (AP)

Advanced Placement (AP), 24.06.2019 22:30

Gneiss is formed. the mineral grains in which granite are flattened under pressure

Answers: 1

Answer

Advanced Placement (AP), 25.06.2019 19:40

What are 3 traits that ruth may price has in the poisonwood bible? how has she adapted to the new situation? what effect has she had on others?

Answers: 2

Answer

Advanced Placement (AP), 25.06.2019 23:20

Which of the following situations would most likely occur if a human-induced event caused the ocean water to become the same temperature around the world? deep ocean current circulation would increase salt distribution around the world's oceans. surface ocean current circulation would distribute heat around land masses at a faster rate. new, fresher water would float on top of dense salt water and limit thermohaline circulation. some land masses in the northern hemisphere would start to warm up over time, melting snow and ice. runoff of surface freshwaters and rainfall would no longer have an effect on the salinity of ocean waters.

Answers: 2

Answer

Advanced Placement (AP), 26.06.2019 00:00

Atown located beside a river derives a large percentage of its revenues each year from the local logging industry. however, heavy traffic to and from the logging sites has increased pollution and contributed to soil erosion. this has also resulted in the loss of native bird species in the logged forests. which of the following is the most sustainable solution to this problem? protecting certain forested areas to allow the birds to recover relocating the equipment and vehicles to new forests for logging relocating the birds to new forests away from the town introducing new bird species to replace the species that have been lost reducing the number of trucks traveling through the forest by 10 percent

Answers: 2

Answer

You know the right answer?

A firm produces and sells a product with a contribution margin of $32 per unit. The firm is presentl...

Questions