MATHEMATICS COLLEGE

Kent Co. manufactures a product that sells for $60.00. Fixed costs are $285,000 and variable costs are $35.00 per unit. Kent can buy a new production machine that will increase fixed costs by $15,900 per year, but will decrease variable costs by $4.50 per unit. What effect would the purchase of the new machine have on Kent's break-even point in units?

Answers

Answer 1

Answer:

0riginal break even point:

285000/ 60/35 = $166,250

New break even point = new fixed costs / ( selling price - variable cost/ selling price)

New break even point = 285,000 + 15,900. / ( 60-( 35-4.50)/60

300,900 / 60-30.50/60 = $612,000

The new break even point increases.

Answer 2

Answer:

Final answer:

With the new machine, Kent Co.'s break-even point in units would decrease, from 11,400 to 10,200 units. Despite increasing fixed costs, the new machine drives down variable costs, effectively lowering the total number of units needed to cover costs.

Explanation:

The concept under consideration here is the break-even point calculation in unit terms. The break-even point (units) is calculated by dividing the total fixed costs by the contribution margin per unit, which is sales price per unit minus variable cost per unit.

Currently, Kent Co.'s break-even point can be found using its original costs:

Fixed costs: $285,000
Sales price per unit: $60
Variable cost per unit: $35
Contribution margin per unit: $60 - $35 = $25
Break-even point (units): $285,000 / $25 = 11,400 units

If Kent were to purchase the new machine, its costs would alter as follows:

New fixed costs: $285,000 + $15,900 = $300,900
New variable cost per unit: $35 - $4.50 = $30.50
New contribution margin per unit: $60 - $30.50 = $29.50
New break-even point (units): $300,900 / $29.50 = 10,200 units

Thus, purchasing the new machine would in fact lower Kent Co.'s break-even point to 10,200 units, thereby improving its cost efficiency.

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Related Questions

In a study of government financial aid for college students, it becomes necessary to estimate the percentage of full-time college students who earn a bachelor's degree in four years or less. Find the sample size needed to estimate that percentage. Use a 0.02 margin of error and use a confidence level of 99%. Complete parts (a) through (c) below.a. Assume that nothing is known about the percentage to be estimated.n = ________b. Assume prior studies have shown that about 55% of full-time students earn bachelor's degrees in four years or less.n = _______c. Does the added knowledge in part (b) have much of an effect on the sample size?
Help please points and brainlest!!
A bag contains 10 w h i t e marbles, 5 g r e e n marbles, 6 y e l l o w marbles. If two different marbles are drawn from the bag , what is the probability of drawing a w h i t e marble then a y e l l o w marble?
If the level of significance of a hypothesis test is raised from .01 to .05, the probability of a Type II error a. will not change. b. will increase. c. will also increase from .01 to .05. d. will decrease.
ANSWER ASAP:Shayla wants to buy some CDs that each cost $14 and a DVD that costs$23. She has $65 that she is able to spend. Which equation can be used todetermine how many CDs Shayla could buy?

HELP PLEASE An officer building 55 ft tall cast a shadow 30 ft long. How tall is a person standing nearby who cast a shadow 3 ft long

Answers

Answer:

About 5.52 feet tall.

Step-by-step explanation:

Divide 55/30. You will get 1.84. Then multiply 3 by 1.84 to get the answer :)

Determine a region of the xy-plane for which the given differential equation would have a unique solution whose graph passes through a point (x0, y0) in the region. (x2 + y2)y' = y2 1. A unique solution exists in the region y ≥ x.
2. A unique solution exists in the entire xy-plane.
3. A unique solution exists in the region y ≤ x.
4. A unique solution exists in the region consisting of all points in the xy-plane except the origin.
5. A unique solution exists in the region x2 + y2 < 1.

Answers

A unique solution exists in the region consisting of all points in the xy-plane except the origin.

The correct option is 4.

The given differential equation is:

(x² + y²)y' = y²

The equation can be rewritten as:

$x^2 + y^2 (dy)/(dx) = y^2$

We need to determine a region of the xy-plane for which the differential equation would have a unique solution whose graph passes through a point (x₀, y₀) in the region.

To determine the region, we can use the existence and uniqueness theorem for first-order differential equations.

According to the theorem, a unique solution exists in a region if the differential equation is continuous and satisfies the Lipschitz condition in that region.

To check if the differential equation satisfies the Lipschitz condition, we can take the partial derivative of the equation with respect to y:

dy/dx = y / (x² + y²)

The partial derivative is continuous and bounded in the entire xy-plane except at the origin (x=0, y=0).

Therefore, the differential equation satisfies the Lipschitz condition in the entire xy-plane except at the origin.

Since the differential equation is continuous in the entire xy-plane, a unique solution exists in any region that does not contain the origin. Therefore, the correct answer is:

A unique solution exists in the region consisting of all points in the xy-plane except the origin.

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Final answer:

The differential equation will have a unique solution in the entire xy-plane except at the origin, as both the function and its partial derivatives are continuous and well-defined everywhere except at that point.

Explanation:

To determine a region of the xy-plane where the differential equation (x2 + y2)y' = y2 has a unique solution passing through a point (x0, y0), we need to consider where the function and its derivative are continuous and well-defined. According to the existence and uniqueness theorem for differential equations, a necessary condition for a unique solution to exist is that the functions of x and y in the equation, as well as their partial derivatives with respect to y, should be continuous in the region around the point (x0, y0).

We note that both the function (x2 + y2)y' and its partial derivative with respect to y, which is 2y, are continuous and well-defined everywhere except at the origin where x = 0 and y = 0. Therefore, a unique solution exists in the region consisting of all points in the xy-plane except the origin.

From the given options, the correct answer is:

4. A unique solution exists in the region consisting of all points in the xy-plane except the origin.

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When are two angles called complements of one another? a. when together they are equal to 180 degrees c. when together they are equal to an acute angle b. when together they are equal to a right angle d. when together they are equal to an obtuse angle

Answers

hola!

Two angles are said to be complements of one another only when:
→ Makes a right angle
→ They add to 90 degrees

Thus,
According to above. statement!

Option [ B ] :
When together they are equal to a right angle is CORRECT!

hope it helps!

b.) complementary angles add up to 90 degrees

In a poll conducted by the Gallup organization in April 2013, 48% of a random sample of 1022 adults in the U.S. responded that they felt that economic growth is more important than protecting the environment. We can use this information to calculate a 95% confidence interval for the proportion of all U.S. adults in April 2013 who felt that economic growth is more important than protecting the environment. Make sure to include all steps.

Answers

Answer:

The 95% confidence interval is $0.449 < p < 0.48 + 0.511$

Step-by-step explanation:

From the question we are told that

The sample proportion is $\r p = 0.48$

The sample size is $n = 1022$

Given that the confidence level is 95% then the level of significance is mathematically evaluated as

$\alpha = 100 - 95$

$\alpha = 5 \%$

$\alpha = 0.05$

Next we obtain the critical value of $(\alpha )/(2)$ from the z-table , the value is

$Z_{(\alpha )/(2) } =Z_{(0.05 )/(2) }= 1.96$

The reason we are obtaining critical value of $(\alpha )/(2)$ instead of $\alpha$ is because

$\alpha$ represents the area under the normal curve where the confidence level interval ( $1-\alpha$ ) did not cover which include both the left and right tail while $(\alpha )/(2)$ is just the area of one tail which what we required to calculate the margin of error

NOTE: We can also obtain the value using critical value calculator (math dot armstrong dot edu)

Generally the margin of error is mathematically represented as

$E = Z_{(\alpha )/(2) } * \sqrt{(\r p (1- \r p ))/(n) }$

substituting values

$E = 1.96* \sqrt{(0.48 (1- 0.48 ))/(1022) }$

$E = 0.03063$

The 95% confidence interval is mathematically represented as

$\r p - E < p < \r p + E$

substituting values

$0.48 - 0.03063 < p < 0.48 + 0.03063$

$0.449 < p < 0.48 + 0.511$

Suppose the sequence StartSet a Subscript n Baseline EndSet is defined by the recurrence relation a Subscript n plus 1equalsnegative 2na Subscript n, for nequals1, 2, 3,..., where a1equals5. Write out the first five terms of the sequence.

Answers

Answer:

-10, 40, -240, 1,920 and -19, 200

Step-by-step explanation:

Given the recurrence relation of the sequence defined as aₙ₊₁ = -2naₙ for n = 1, 2, 3... where a₁ = 5, to get the first five terms of the sequence, we will find the values for when n = 1 to n =5.

when n= 1;

aₙ₊₁ = -2naₙ

a₁₊₁ = -2(1)a₁

a₂ = -2(1)(5)

a₂ = -10

when n = 2;

a₂₊₁ = -2(2)a₂

a₃ = -2(2)(-10)

a₃ = 40

when n = 3;

a₃₊₁ = -2(3)a₃

a₄ = -2(3)(40)

a₄ = -240

when n= 4;

a₄₊₁ = -2(4)a₄

a₅ = -2(4)(-240)

a₅ = 1,920

when n = 5;

a₅₊₁ = -2(5)a₅

a₆ = -2(5)(1920)

a₆ = -19,200

Hence, the first five terms of the sequence is -10, 40, -240, 1,920 and -19, 200

Identify the surface with the given vector equation. r(s, t) = s sin 4t, s2, s cos 4ta. plane
b. hyperbolic paraboloid
c circular paraboloid
d.circular cylinder
e. elliptic cylinder

Answers

Following are the calculation to the given equation:

Given vector equation:

$\to r(s, t)= (s \sin 4t,s^2, s \cos 4t)$

The corresponding parametric equations for the given surface is given by,

$x=s \sin 4t\n\n y =s^2\n\n z=s \cos 4t$

For any point (x,y,z) we have that,

$x^2+z^2 = (s \sin 4t)^2 +(s \cos 4t)^2$

$= s^2 \sin^2 4t +s^2 \cos^2 4t \n\n= s^2 (\sin^2 4t+cos^2 4t) \n\n= s^2 (1) \n\n=s^2\n\n=y \n$

So, after eliminating the parameters, we get, $x^2 +z^2 = y$

Therefore, the answer is "Option c".

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Final answer:

The surface represented by the given vector equation r(s, t) = s sin 4t, s2, s cos 4t is a circular cylinder. This can be inferred from the structure of the equation and the characteristics of the represented shapes.

Explanation:

The surface represented by the given vector equation,

r(s, t) = s sin 4t, s2, s cos 4t

, is a type of cylindrical surface due to the structure of the equation. This can be identified by the s terms being tied to sin/cos functions and an independent s^2 term. This shows that the s variable is acting as a 'driver' of the shape, while t coordinates the rotation. Owing to the periodic sin and cos functions in the vector equation, the surface does not lie in a single plane, ruling out the option of a plane. It also does not exhibit features of a paraboloid or hyperbolic paraboloid. Hence, it's shown that the vector equation represents a

circular cylinder

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Foster makes sandwiches at a deli. There are 10 1/2 pounds of turkey at the deli. How many 1/4 -pound turkey sandwiches can he make?

Determine whether [1 0 3 , −3 1 −7 , 5 −1 13] is a basis for set of real numbers R cubed 3. If the set is not a basis, determine whether the set is linearly independent and whether the set spans set of real numbers R cubed 3.

Based on the sample results, about what proportion of the population would you expect to prefer Merchant D?A. about 0.03B. about 0.30C. about 0.12D. about 0.60