The cost C of producing x footballs per day is given by the

The cost, C of producing x footballs per day is given by the formula:

C = 1200 + 50x - .05x², find the rate of change of C with respect to x (called marginal cost) when 1000 footballs are being produced each week (5day week)

Solution

1000 footballs are being produced each week in a 5 day week

So number of footballs produced each day =1000/5=200

So, x=200

Rate of change of C w.r.t. x is

dC/dx=50-0.1x

At, x=200 this becomes

dC/dx=50-0.1*200=30 footballs per day