Answer:
R(p) = -2400p² + 10600p
Step-by-step 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
