8
algebra

A company produces widgets. Fixed costs are $500 per day, and each widget costs $3 to produce. Widgets sell for $8 each. How many widgets must be sold to break even?

A

80 widgets

B

100 widgets

C

120 widgets

D

150 widgets

Correct Answer: B

Choice B is the correct answer. Break-even occurs when Cost = Revenue.

Analysis: Let xx = number of widgets

  • Total Cost: C=500+3xC = 500 + 3x (fixed + variable)
  • Total Revenue: R=8xR = 8x

Step 1: Set Cost = Revenue: 500+3x=8x500 + 3x = 8x500=5x500 = 5xx=100x = 100

Solution: 100 widgets

Verification:

  • Cost: 500+3(100)=800500 + 3(100) = 800
  • Revenue: 8(100)=8008(100) = 800 ✓

💡 Strategic Tip: Break-even analysis: find where revenue equals total cost (fixed + variable).

Choice A is incorrect because at 80: Cost = 740,Revenue=740, Revenue = 640 (loss).

Choice C is incorrect because at 120: Cost = 860,Revenue=860, Revenue = 960 (profit, past break-even).

Choice D is incorrect because at 150: Cost = 950,Revenue=950, Revenue = 1200 (profit, past break-even).

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Linear Functions Set 56