cost price + profit = selling price

120,000 + 4n + 200,000 = 20n

16n = 320,000
n = 20,000 (A)

Let x be the items being produced
CP = 4x
SP = 20x
Profit = 16x
Since the fixed cost of 120000 needs be recovered along with making a 200000$ profit, the total profit that needs to be made is 320000$

16x = 320000
x = 20000 items(Option A)
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I couldn't "see" the equation within 20 seconds, though I knew I was close. I decided to test values where x = the number of items to be produced and sold.

Option C looks less than fun.

1. Start with D, where x = 5000

Total cost (TC): $120,000 + ($4)*(5,000) = $140,000

Total revenue (TR): ($20)*(5,000) = $100,000

Gross profit = (TR - TC) = -$40,000 ... So x = 5,000 is much too small.

2. Try A, x = 20,000

TC: $120,000 + ($4)*(20,000) = $200,000

TR: ($20)*(20,000) =$400,000

$400,000 - $200,000 = $200,000 profit. Correct.

Answer A
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Solution

Given:

• Greg’s production costs includes of annual fixed costs and variable costs.
• Annual fixed costs = $120,000
• Variable costs= $4 per item.
• Greg’s selling price per item = $20

To find:

• The number of items, Greg’s must produce and sell to earn an annual profit of $200,000

Approach and Working

• Production cost= Fixed cost+ Variable cost

o Product cost= 120,000+ 4*n, where n is the number of item produced.

• Selling price of n items= 20*n
• Profit = 200,000
• 20*n - (120,000 + 4*n) = 200,000
• 16 * n = 320,000
• n = 20,000

Correct answer: Option A
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Hello EgmatQuantExpert !

• Selling price of n items= 20*n
• Profit = 200,000
• 20*n- (120,000+ 4*n) = 200,000
20*n -120,000 - 4*n)
• 16n= 320,000
• N= 20,000[/list]

I guess it should be inside the parenthesis, right?

Kind regards!

Hi,

Thanks for pointing it out. We missed the parenthesis, but the answer remains the same.

Regards,
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