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Akimi4 [234]
3 years ago
9

A company manufactures its product at a cost of $0.50 per item and sells it for $0.85 per item daily overhead is $600 how many i

tems must be manufactured each day in order for the company to break even
Mathematics
1 answer:
Nataly_w [17]3 years ago
4 0

so the company has an overhead of $600, usually that involves premises leasing and industrial equipment for the manufacturing of the product, that's cost.  The cost to make each item is 50 cents, so if the company produces "x" items, their cost is 0.5x total.

so our cost equation C(x) = 0.5x + 600   <---- items' cost plus overhead.

the company sells the product for 85 cents, so if they sell "x" items, their total revenue or income will be 0.85x.

so our revenue equation is simply R(x) = 0.85x.

as you already know, the break-even point is when.... well, you break even, no losses but no gains either, how much you take in is the same amount that you shelled out, namely R(x) = C(x).

\bf \stackrel{R(x)}{0.85x}=\stackrel{C(x)}{0.5x+600}\implies 0.35x=600\implies x=\cfrac{600}{0.35} \\\\\\ x\approx 1714.285714285714\implies \stackrel{\textit{rounded up}}{x=1714}

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laila [671]

Answer:

5 trees should be planted to maximize the yield per acre,

The maximum yield would be 1250

Step-by-step explanation:

Given,

The original number of trees per acre = 20,

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Let x be the times of increment in number of trees,

So, the new number of trees planted per acre = 20 + x

∵ for each additional tree planted per acre, the average yield per tree drops 2 pounds,

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Thus, the total yield per acre,

Y(x) = (20+x)(60-2x)

Differentiating with respect to t ( time ),

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Again differentiating with respect to t,

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⇒ 20 = 4x

⇒ x = 5,

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Hence, Y(x) is maximum for x = 5,

And, maximum value of Y(x) = (20+5)(60 - 10) = 25(50) = 1250,

i.e. 5 trees should be planted to maximize the yield per acre,

and the maximum yield would be 1250 pounds

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