Widget Wonders produces widgets. They have found that the cost, c(x), of making x widgets is a quadratic function in terms of x. The company also discovered tha
Question
The company also discovered that it costs $29 to produce 2 widgets, $115 to produce 4 widgets, and $757 to produce 10 widgets.
How much does it cost to make 3 widgets?
1 Answer

1. User Answers SaniShahbaz
Answer:
The total cost to make 3 widgets is $64.
Stepbystep explanation:
As cost is give by quadratic function such as [tex]c(x) = ax^2 + bx + d[/tex]
As it costs $29 to produce 2 widgets. So,
[tex]c(2) = a(2)^2 + b(2) + d[/tex]
[tex]29= 4a+2b+d ....[A][/tex]
As it costs $115 to produce 4 widgets. So,
[tex]c(4) = a(4)^2 + b(4) + d[/tex]
[tex]115= 16a+4b+d ....[B][/tex]
As it costs $757 to produce 10 widgets. So,
[tex]c(10) = a(10)^2 + b(10) + d[/tex]
[tex]757= 100a+10b+d ....[C][/tex]
In order to find the values of a, b, c and d, we have to equations [A], [B] and [C]
Subtracting Equation [A] from [B] and [B] from [C]
12a + 2b = 86 ........[D]
84a + 6b = 642 ........[E]
Multiplying Equation [D] by 3 and subtracting from [E]
84a + 6b + 3(12a + 2b) = 642  86
48a = 384
a = 8
Putting value of a = 8 in equation [D]
12(8) + 2b = 86
96 + 2b = 86
2b = 10
b = 5
Substituting the value of a = 8 and b = 5 in Equation [A].
29= 4a+2b+d
29 = 4(8) + 2(5) + d
29 = 32  10 + d
d = 29 + 10  32
d = 7
The required form of equation can be obtained by substituting a = 8, b = 5 and d = 7 in the cost equation. So,
[tex]c(x) = 8x^2  5x + 7[/tex] is the required form of equation.
Therefore, the total cost to make 3 widgets will be:
Putting x = 3 in [tex]c(x) = 8x^2  5x + 7[/tex]
[tex]c(3) = 8(3)^2  5(3) + 7[/tex]
[tex]c(3) = 72  15 + 7[/tex]
[tex]c(3) = 64[/tex]
Hence, the total cost to make 3 widgets is $64.
Keywords: quadratic equation, cost
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