Two Word Problems Need Help

Question

Please help me solve these TWO problems.

1. A golf ball is hit from the ground, and its height can be modeled by the equation h(t) = -16t^2 + 128t, where h(t) represents the height (in feet) of the ball t seconds after contact. What will the maximum height of the ball be?
2. A company that produces video games has hired you to set the sale price for its newest game. Based on production costs and consumer demand, the company has concluded that the equation p(x) = -0.3x^2 + 45x - 1000 represents the profit p (in dollars) for x individual games sold. What will the company’s profit be if it sells 100 games?

Answer 1

h(t) =-16t^2 + 128t

h'(t) = -32t +128 =0

t = 128/32 = 4 seconds to reach maximum height

max height =-16(4)^2 +128(4)

= (128-64)(4) = 64(4) = 256 feet

p(x)= -.3x^2+45x-1000

p(100)=-.3(100)^2 +45(100) -1000

=-3000+4500-1000

= $500 = profit when 100 are sold

max profit is when p'(x) = -.6x +45 =0

x =45/-.6 = 75

p(75) = -.3(75)^2 +45(75) -1000

= (45-22.5)(75) = 22.5(75) = 1607.50 = $1,650=max profit

the profit function graphed is a downward opening parabola

with vertex at (75, 1650)

another point on the parabola is (100, 500)

another point on the parabola is (50, 500)

profit is $500 at either x=50 or 100 games sold