Question

A maize farmer produces using two inputs labour(L) and fertilizer(K) the farmers total cost function is given as TC=(0.5r+√(rw)+0.5w)q, where q is output of maize in bags and r andw are the unit prices of fertilizer and labour respectively. Fertilizer is measured in bags. If the farmer's objective is to produce sh 10000 bags of maize, and fertilizer costs sh 1600 per bag and labour costs sh 100 per hour, how many bags of fertilizer will the farmer require to minimize cost?

Answer 1

TC = (0.5r + √(rw) + 0.5w)q
If the farmer's objective is to produce sh 10000 bags of maize, and fertilizer costs sh 1600 per bag and labour costs sh 100 per hour, then the amount of bags of fertilizer that the farmer will require to minimize cost is:
TC = (0.5r + √(rw) + 0.5w)q = (0.5*1600 + √(1600*100) + 0.5­*100)*10000 = (800 + 400 + 50)*10000 = sh 12,500,000.
The amount of bags of fertilizer can't be found, because we have no information about production function.