Download Precal 4.4 Quadratic Models - Level E Name 1. A toy store sells

Precal 4.4 Quadratic Models - Level E
Name ____________________________
1. A toy store sells stuffed teddy bears at a price of p dollars per unit and the number x of these stuffed
teddy bears is given by the demand equation p = - 1 x + 35
10
a) Express the revenue R as a function of x (remember: R = xp).
b) What is the quantity x that maximizes revenue?
c) What is the maximum revenue?
d) What price should the toy store charge to maximize revenue?
(back)
Precal 4.4 Quadratic Models - Level E
Name ____________________________
1. A toy store sells stuffed teddy bears at a price of p dollars per unit and the number x of these stuffed
teddy bears is given by the demand equation p = - 1 x + 35
10
a) Express the revenue R as a function of x (remember: R = xp).
b) What is the quantity x that maximizes revenue?
c) What is the maximum revenue?
d) What price should the toy store charge to maximize revenue?
(back)
2. A parabolic cable suspension bridge with weight uniformly distributed along its length has twin towers that
extend 70 meters above the road surface and are 900 meters apart. The cables touch the road surface at the center
of the bridge. (a) Draw an illustration of the situation and label an origin and a vertex. (b) Write the equation of
the parabola formed by the cable. (c) Use the equation to find the height of the cable at a point 225 meters from
the center of the bridge.
3. Sally has 450 meters of fencing and wants to enclose a rectangular plot that borders on a river. Sally will not
fence the side along the river.
a) Express the area A of the rectangle as a function
of width w.
b) For what value of width w is the area the largest?
c) What is the maximum area that can be enclosed?
2. A parabolic cable suspension bridge with weight uniformly distributed along its length has twin towers that
extend 70 meters above the road surface and are 900 meters apart. The cables touch the road surface at the center
of the bridge. (a) Draw an illustration of the situation and label an origin and a vertex. (b) Write the equation of
the parabola formed by the cable. (c) Use the equation to find the height of the cable at a point 225 meters from
the center of the bridge.
3. Sally has 450 meters of fencing and wants to enclose a rectangular plot that borders on a river. Sally will not
fence the side along the river.
a) Express the area A of the rectangle as a function
of width w.
b) For what value of width w is the area the largest?
c) What is the maximum area that can be enclosed?