The fresh milk market in Honolulu is purely competitive. The typical production cost is defined through a a cubic cost schedule as given below.
Y C
0 200
1 397.06
2 518.48
3 582.62
4 607.84
5 612.5
6 614.96
7 633.58
8 686.72
9 792.74
10 970
Find (a) the cubic equation that describes the production function of milk, (b) find the output of milk that maximizes profit if the price of milk is $150/ton, © find the maximum profit.