4
algebra

Maximize P=3x+2yP = 3x + 2y subject to x+y5x + y \leq 5, x0,y0x \geq 0, y \geq 0.

A

1515

B

1010

C

1313

D

1212

Correct Answer: A

Choice A is the correct answer. Check vertices.

  1. Vertices: (0,0),(5,0),(0,5)(0,0), (5,0), (0,5).
  2. Evaluate P:
  • (0,0):0(0,0): 0
  • (5,0):3(5)+0=15(5,0): 3(5) + 0 = 15
  • (0,5):0+2(5)=10(0,5): 0 + 2(5) = 10
  1. Max: 15.

💡 Strategic Tip: The maximum usually occurs at a vertex.

Choice B is incorrect.Choice C is incorrect.Choice D is incorrect.