Question

photo Necessities produces camera cases. They have found that the cost, c(x), of making x camera cases is a quadratic function n terms of x. The company also discovered that it cost $25 to produce 2 camera cases, $59 to produce 4 camera cases, and $305 to produce 10 camera cases. Find the total cost of producing 5 camera cases. Find the total cost of producing 5 camera cases

Answer 1

The quadratic equation is\[c(x)=ax^2+bx+c\]
where a,b, c are constants
When x=2
\[c(2)=4a+2b+c=25.............(1)\]
When x=4
\[c(4)=16a+4b+c=59...........................(2)\]
When x=10
\[c(10)=100a+10b+c=305........................(3)\]
Solving for a, b and c in equations (1). (2) and (3)
From (1) and (2)
\[12a+2b=34\]
\[6a+b=17........................(4)\]
From (1) and (3)
\[96a+8b=280\]
\[12a+b=35.................(5)\]
From (4) and (5)
\[6a=18\]
\[a=3\]
\ \[c=59-48+4=15\] The quadratic equation is \[c(x)=3x^2-x+15\] Finally, the cost of 5 camera cases is \[c(5)=3*25-5+15=85\] The answer is 85$