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Linear Equations in One Variable

SAT Math· difficulty 5/5

The cost of producing xx units is C(x)=1000+25xC(x) = 1000 + 25x and revenue is R(x)=50xR(x) = 50x. What is the minimum number of units to produce a profit of at least \2{,}000$?

  • A

    150

  • B

    200

  • C

    100

  • D

    120

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Explanation

Profit P(x)=50x−(1000+25x)=25x−1000P(x) = 50x - (1000 + 25x) = 25x - 1000. Need 25x−1000≥200025x - 1000 \geq 2000 → x≥120x \geq 120.

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