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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:

Writing the inequality, we have;

420.56+32.43x\leq680

the solution to the inequality is;

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Explanation:

Given that Natalie has $680 to spend at a bicycle store for some new gear and biking outfits.

Total spending must not exceed $680

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Total spending is;

\begin{gathered} 383.33+2(7.61)+22.01+32.43(x) \\ 420.56+32.43x \end{gathered}

Writing the inequality, we have;

420.56+32.43x\leq680

we can now solve the inequality;

\begin{gathered} 420.56+32.43x\leq680 \\ \text{subtract 420.56 from both sides;} \\ 420.56-420.56+32.43x\leq680-420.56 \\ 32.43x\leq259.44 \\ \text{divide both sides by 32.43} \\ \frac{32.43x}{32.43}\leq\frac{259.44}{32.43} \\ x\leq8 \end{gathered}

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