The cost. C(x), of making x camera cases is a quadratic function in terms of x.

Question

The company also discovered that it costs $28 to produce 2 camera cases, $50 to produce 4 camera cases, and $140 to produce 10 camera cases. Find the total cost of profucing 12 camera cases.

Answer 1

Each point on this quadratic function will be of the form (x,C).  The problem gives three points:

 

(2,28), (4,50) and (10,140).  Each of these points will satisfy the quadratic function, C = ax²+bx+c.  Substituting the values of our three given points into the quadratic function, we can solve systems of equations in order to find a, b, and c:

 

28 = a(2)²+b(2)+c ----> 28 = 4a + 2b + c

50 = a(4)²+b(4)+c ----> 50 = 16a + 4b + c

140 = a(10)²+b(10)+c ----> 140 = 100a + 10b + c

 

Subtracting the first equation from the second equation, we obtain 22 = 12a + 2b ----> 11 = 6a + b

Subtracting the second equation from the first equation, we obtain 90 = 84a + 6b ----> 15 = 14a + b

 

We can now subtract the top equation from the bottom one to obtain 4 = 8a.  From this, we find that a = 1/2.

 

We can then substitute a = 1/2 into the equation, 11 = 6a + b ----> 11 = 6(1/2) + b ----> 11 = 3 + b ----> b = 8.

 

We now use one of the original three equations to solve for c:

 

28 = 4a + 2b + c

28 = 4(1/2) +2(8) + c

28 = 2 + 16 + c

10 = c

 

Therefore, the quadratic equation is:

 

C(x) = 1/2x² + 8x + 10

 

Then, the total cost of making 12 camera cases would be:

 

C(12) = 1/2(12)²+ 8(12) + 10

C(12) = 1/2(144) + 96 + 10

C(12) = 72 + 96 + 10

C(12) = 178

 

Therefore, the cost to make 12 camera cases would be $178.

 

I hope this helps!

 

Maria Tilmos

Answer 2

C(x) is quadratic in terms of x, therefore C(x)=a*x²+b*x+c

 

Find three linear equations using the information given:

 

Info 1: cost of 2 cases is $28, therefore C(2)=a*2²+b*2+c=4a+2b+c=28 -> equation 1: 4a +2b+c=28

 

Set up the other two equations in a similar way, then solve the system of equations for a,b,c.

 

Then you get C(x) and can evaluate it for x=12.

Answer 3

We use the information to produce a quadratic equation.

 

Let x = the number of cases produced

Let C(x) = cost

 

 

First create a table.

 

x          C(x)

 

2         28

4         50

10       140

 

 

Use the info to create a rule.  This rule will be the function.  Once you have that function, use it to find the cost of 12 cases.

 

 

If you have a graphing calculator, I can show you how to get that function easily.