For a cost function I have been given the following information:
fixed costs: 65\$
Production of 10 elements costs: 80\$
Production of 20 elements costs: 87\$
Producing 1 more when producing 10 elements costs 1\$
[Edit:] And I know that it has to be a cubic function.
And have arrived at the following cost function:
[Edit:] (Which I know is correct, because it is given as a control point.)
I have the revenue function:
Which leads to the profit function:
Now another product should be produced where
variable cost per element is higher by 1.1\$
fixed costs for the new product is 20\$
The profit function for the new product is given as:
All that is left for me to do is prove that this is correct.
Any idea how to do this?
I have calculated variable costs for the original product:
$cv_1(10) = 15$
$cv_1(20) = 22$
so I got variable costs for the second product:
$cv_2(10) = 26$
$cv_2(20) = 44$
And have tried to adapt the original system of equations with these values, and solve them, but I am not arriving at the correct equatation.