Question

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Answer 1

(a)

R(p) = -8p² + 1328p

R(50) = -8(50)² + 1328(50)

         = -8(2500) + 66,400

         = -20,000 + 66,400

         = 46,400

R(70) =  -8(70)² + 1328(70)

         = -8(4900) + 92,960

         = -39,200 + 92,960

         = 53,760

R(90) =  -8(90)² + 1328(90)

         = -8(8100) + 119,520

         = -64,800 + 119,520

         = 54,720

(b) R(p) = -8p² + 1328p       NOTE: maximum is the vertex

              a=-8, b=1328

p = $\frac{-b}{2a} = \frac{-(1328)}{2(-8)} = \frac{-1328}{-16}$ = 83

(c)

R(83) =   -8(83)² + 1328(83)

         = -8(6889) + 110,224

         = -55,112 + 110,224

         = 55,112