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Linear Inequalities in One or Two Variables

SAT Math· difficulty 5/5

A factory produces widgets at 3.50perunitwithafixedcostof3.50 per unit with a fixed cost of 5{,}000. They sell at 8perunit.Howmanywidgetsmusttheyselltoearnatleast8 per unit. How many widgets must they sell to earn at least 10{,}000 profit?

  • A

    3{,}334

    check_circle
  • B

    3{,}000

  • C

    3{,}500

  • D

    4{,}000

Explanation

Profit: 8n−3.50n−5000≥100008n - 3.50n - 5000 \geq 10000. So 4.5n≥150004.5n \geq 15000 and n≥3333.3‾n \geq 3333.\overline{3}. Smallest integer: 33343334.

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