Question

The weekly revenue of a business selling gummy bear bags is a function of price. Weekly revenue is $10,816 when the price is $1.60 but is $9,344 when the price is $3.20 Find a quadratic model that fits this information. Also know that the revenue is $0 if the price is $0. Let p = the price of a bag of gummy bears. Then: Revenue = R ( p ) =

Answer 1

R(p) = -2400p² + 10600p

Explanation:

p = The price of a bag of gummy bears

R(p) = Revenue

A quadratic model for the revenue R(p) can be written as:

R(p) = ap² + bp + c...............(1)

When R = $10,816 p = $1.60

10816 = a(1.60)² + b(1.60) + c

10816 = 2.56a + 1.6b + c...........(2)

When R = $9,344 p = $3.20

9344 = a(3.20)² + b(3.20) + c

9344 = 10.24a + 3.20b + c............(3)

When R = $0, p = $0

0 = a(0)² + b(0) + c

c = 0

Therefore, equations (1) and (2) become:

10816 = 2.56a + 1.6b..........(4)

9344 = 10.24a + 3.20b.......(5)

From the two simultaneous equations above:

a = -2400, b = 10600

Therefore the quadratic model in equation becomes:

R(p) = -2400p² + 10600p