# Question: hi i need help with this question quota farmer who...

###### Question details

Hi! I need help with this question:

"A farmer who keeps both chickens and ducks has to maximise his revenue and is faced with the following constrained optimisation problem:

He can only keep a total 6900 animals (chickens and ducks) on his land for the "free-range" certification for his produce. The buyers want a bulk discount to apply on the price of the chickens and ducks according to the formulae:

Price per chicken = $7.50-loge (number of chickens)

and

Price per duck = $9.40 - loge (number of ducks)

Using Lagrange Multipliers, calculate the number of chickens and ducks the farmer should keep (to nearest whole number)

Calculate the price per chicken and the price per duck for the optimal solution found in part (a). What do you notice? Explain why this is the case and use this to confirm the results you found in part (a)