Each cow weighs 300kg. The cost of maintaining a cow is 20€ per day. The rate of change of the cows weight is 4kg a day. The market price is currently 50€ per kg and it is falling 50 cents a day. How much time should the cattleman wait to sell the cows? How much extra money does he make by waiting?
Profit maximization through differentiation (cattle)
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1 Answers
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HINT: $$ W = 300 + 4d, $$ $$ P = 50W - \frac{d}{2} - 20d, $$ Plug the expression for $W$ into the expression for $P$ and obtain an expression for $P$ in terms of $d$. Differentiate this and set to $0$ to find the maximum.