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Akimi4 [234]
2 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]2 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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Find Sales Price of 5 gallons of ice-cream:
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Sales price of Fruity Tooty = $6.00
Sales price of Peanut Butter = $5 x 2 = $10.00
Sales price of Rocky Road = $5.25 x 2 = $10.50
Total Sales Per 5 gallon = $6 + $10 + $10.50 = $26.50

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Find Variable Cost of 5 gallons of ice-cream:
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Variable Cost of Fruit Tooty = $5.25
Variable Cost of Peanut Butter = $4.50 x 2 = $9.00
Variable Cost of Rocky Road = $4 x 2 = $8.00
Total Variable Coast = $5.25 + $9 + $8 = $22.25

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Fixed Cost Given:
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Fixed Cost = $7500

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Define x:
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Let x be the number of 5 gallons that need to be sold to breakeven:

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Find x:
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26.50x = 7500 + 22.25x

26.50x - 22.25x = 7500

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x = 7500 ÷ 4.25

x = 1764.7 (Nearest tenth)

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Find the number of gallons of ice-cream needed:
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Total number of 5 gallons needed = 1764.7

Total gallons needed = 1764.7 x 5 =8823.5

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Answer: I sceam needs to sell 8823.5 gallons of ice cream to break even.
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