Question: You have a summer internship with a swine company. From their scientists, you obtain the following production function for weight gain for 30 lb feeder pigs:

G = -950 + 12C + 10S – 0.06C² – 0.08S² + 0.03CS,

where G is pounds of gain, C is pounds of ground corn consumed and S pounds of soybean meal consumed. If the price of hogs is $100/cwt (hundredweight), the price of ground corn is $280/ton, and the price of soybean meal is $680/ton, answer the following questions:

a) How much ground corn and soybean meal is it economically optimal to feed the feeder

pigs? Don’t forget to convert prices to $/lb and to check the second order conditions.

b) When feeding these levels, what is the gain for the feeder pigs?

c) When feeding these levels, what is the net return per feeder pig? Assume net return is

\(pG-{{r}_{c}}C-{{r}_{s}}S-120\), where p, \({{r}_{c}}\) and \({{r}_{s}}\) are the prices of hogs, ground corn and soybean meal and 120 is the other costs per pig. Ignore all other costs