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Linear Equations in One Variable

SAT Math· difficulty 5/5

A company's profit model is P(x,y)=8x+12yP(x, y) = 8x + 12y with constraints x+y≤100x + y \leq 100 and 2x+y≤1502x + y \leq 150, x,y≥0x, y \geq 0. The maximum profit occurs at which vertex?

  • A

    (75,0)(75, 0)

  • B

    (50,50)(50, 50)

  • C

    (0,100)(0, 100)

    check_circle
  • D

    (100,0)(100, 0)

Explanation

Check vertices: (0,100)(0, 100): P=1200P = 1200. (50,50)(50, 50): P=400+600=1000P = 400 + 600 = 1000. (75,0)(75, 0): P=600P = 600. (0,0)(0,0): 00. Max at (0,100)(0, 100).

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