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 that it cost $23 to produce 2 widgets, $103 to produce 4 widgets, and $631 to produce 10 widgets.

find the total cost of producing 6 widgets.

The total cost of producing 6 widgets is $231.

Step-by-step explanation:

Given : Widget wonders produces widgets. They have found that the cost, c(x), of making x widgets is a quadratic function in terms of x.

To find : The total cost of producing 6 widgets.

Solution :

Cost is given by

.........[1]

............[2]

...........[3]

Now, we solve equation [1], [2] and [3]

Subtract equation  [2]-[1]  and [3]-[2]

[2]-[1] →    ........[4]

[3]-[2] →    .......[5]

Solving equation [4] and [5] by elimination method,

Multiply equation [4] by 3 and subtract from [5]

Put in equation [4]

Substitute the value of a and b in [1] to get d

Substitute a=6,b=4,d=-9 in the cost equation,

The required equation form is

The total cost of producing 6 widgets.

Put x=6

Therefore, The total cost of producing 6 widgets is $231.