one of the compulsory subjects for final year of Civil Engg. in my college is Structural Optimization. The professor has been guiding us through the various methods used for classical optimization problems.
Recently, we were given the below problem as homework.
A manufacturer produces small refrigerators at a cost of USD60 per unit and sells them toa retailer in a lot consisting of a minimum of 100 units. The selling price is set at USD80per unit if the retailer buys 100 units at a time. If the retailer buys more than 100 unitsat a time, the manufacturer agrees to reduce the price of all refrigerators by 10 cents foreach unit bought over 100 units. Determine the number of units to be sold to the retailerto maximize the profit of the manufacturer.
I tried forming an objective function for it in two ways
Approach 1
Assuming that, number of units manufactured = number of units sold = x1
Profit on each unit is 20USD so total profit = 20*x1 and
Deducting 10 cents for refrigerators beyond 100 units (in USD) = (10/100)*(x1-100)
so we get
f(X) = 20*x1 - 0.1*(x1-100)
= 19.9*x1 + 10
with inequality constraints
g1 = x1>=100
This didn't workout for me as I quickly hit a roadblock when making the conditions, didn't know what to do after making the conditions (I am doubtful about this function).
Approach 2
Assume manufactured units = x1
Units sold = x2
Profit = 80*x2 - 60*x1
Deduction = 0.01(x2-100)
f(X) = 79.9x2 - 60x1 +10
with inequality constraints
g1 = x1>=x2
g2 = x2>=100
Hit a roadblock with this as well, this seems to be caused by my lack of understanding of the subject (it's very new to me).
I don't want someone else to solve it for me but I'd really appreciate it if you could hint at what other approach I should try that would work, instead of these two.