Suppose pigs $($P$)$ can be fed corn$-$based feed $($C$)$ or soybean$-$based feed $($S$)$ such that the production function is P $=2$C $+5$S$.$If the price of corn feed is $$4$ and the price of soybean feed is $$5,$ what is the cost$-$minimizing feed combination producing P $=200?$

$9$

a$.$

C $=100$

b$.$

S $=40$

c$.$

C $=50,$ S $=20$

d$.$

C $=20,$ S $=5$