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vazorg [7]
3 years ago
8

A company’s total cost from manufacturing and selling x units of their product is given by: y = 2x2 – 600x + 49,000. How many un

its should be manufactured in order to minimize cost, and what is the minimum cost?a. (100, $9,000)b. (125, $3,250)c. (150, $4,000)d. (170, $4,800)e. (200, $9,000)
Mathematics
1 answer:
ale4655 [162]3 years ago
3 0

Answer: Option 'c' is correct.

Step-by-step explanation:

Since we have given that

y=2x^2-600x+49000

We need to find the number of units in order to minimize cost.

We first derivative w.r.t. x,

y'=4x-600

For critical points:

y'=0\\\\4x-600=0\\\\4x=600\\\\x=\dfrac{600}{4}\\\\x=150

Now, we will check whether it is minimum or not.

We will find second derivative .

y''=4>0

So, it will yield minimum cost.

Minimum cost would be

y(150)=2(150)^2-600\times 150+49000\\\\y(150)=\$4000

Hence, At 150 units, minimum cost = $4000

Therefore, Option 'c' is correct.

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Answer:

option b is the answer

Step-by-step explanation:

3 0
2 years ago
Help me please!!
Setler [38]

Answer:

3.A

2.59 %

3.B

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6 0
3 years ago
Given the position of the particle, what the position(s) of the particle when it’s at rest
choli [55]

The position function of a particle is given by:

X\mleft(t\mright)=\frac{2}{3}t^3-\frac{9}{2}t^2-18t

The velocity function is the derivative of the position:

\begin{gathered} V(t)=\frac{2}{3}(3t^2)-\frac{9}{2}(2t)-18 \\ \text{Simplifying:} \\ V(t)=2t^2-9t-18 \end{gathered}

The particle will be at rest when the velocity is 0, thus we solve the equation:

2t^2-9t-18=0

The coefficients of this equation are: a = 2, b = -9, c = -18

Solve by using the formula:

t=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}

Substituting:

\begin{gathered} t=\frac{9\pm\sqrt[]{81-4(2)(-18)}}{2(2)} \\ t=\frac{9\pm\sqrt[]{81+144}}{4} \\ t=\frac{9\pm\sqrt[]{225}}{4} \\ t=\frac{9\pm15}{4} \end{gathered}

We have two possible answers:

\begin{gathered} t=\frac{9+15}{4}=6 \\ t=\frac{9-15}{4}=-\frac{3}{2} \end{gathered}

We only accept the positive answer because the time cannot be negative.

Now calculate the position for t = 6:

undefined

6 0
1 year ago
What is the length of 15,409,000 cubic yard in miles? (to<br> the nearest hundred)
cluponka [151]

Answer:

Step-by-step explanation:

The cube root of 15,409,000 = 248.84 yards.

There are 1760 yards in a mile

One edge of a cube = 248.84 / 1760 = .141386 miles.

So a cube would be .00283cubic miles. Your answer does not reach a hundredth place, I don't think.

4 0
3 years ago
How is dividing decimals different from dividing whole numbers?Please answer immediately.
Masteriza [31]
If you divide decimals you have to bring up the decimal point but if you divide whole numbers you dont have any decimal points so you just divide the numbers. Sorry if i didnt help i just wanted to help.
7 0
3 years ago
Read 2 more answers
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