Question

A company produces widgets at plants 1 and 2. It costs 135x1/2 dollars to produce x units at plant 1 and 260x1/3 dollars to produce x units at plant 2. Each plant can produce up to 1,000 units. Each unit produced can be sold for $12. At most 1,700 widgets can be sold. Determine how the company can maximize its profit.

Answer 1

Answer
As higher the production the lower is its cubic root so plant two will produce 1000 quantity and plant 1 will produce remaining (700 units)
so
TC=135*(700)^(1\2)+260*(1000)^(1\3)
=3571.77+2599.99
=6171.76
TR=12*1700

= 20400
Profit = 20400-6171.76
=14228.24

so It will maximize profit by producing maximum quantity from plant 2 and minimum quantity from plant 1.