Gymnast manufactures expensive soccer cleats for sale to col

Gymnast manufactures expensive soccer cleats for sale to college bookstores in runs of up to 500. Its cost (in dollars) for a run of x pairs of cleats is C(x) = 3200 + 5x + 0.1x^2 (0

Solution

Revenue : Total income from producing units.

We have sake price per unit ---- $ 110 per pair

Revenue from sale of x units= 110*x = 110x

a) Revenue = 110x ; for x units

b) Profit = Income -    Cost

= 110x - ( 3200 + 5x + 0.1x^2)

= - 0.1x^2 + 105x -3200 ; for x units

c) He should manufacture x units to have profit i.e Profit > 0

- 0.1x^2 + 105x -3200 > 0

After raitioanlsing decimal numbers we get : -x^2 + 1050x -32000 =0

Roots of the equation are x= 31.41 and x = 1018.58 units

Solution of inequality : 31.41 < x < 1018.58

So, atleast x= 32 pairs should be produced to have profit