# Linear Programming Formulate

A small firm produces three types of wooden lampstands: rounded,angular and rectangular. All types require two hand-crafted processes: cutting and smoothing. Rounded lampstands require 1 hour of cutting and 3 hours of smoothing whereas Angular lampstands require 2 hours of cutting but only 1 hour of smoothing. Rectangular lampstands require 2 hours of cutting and 2 hours of smoothing. The firm has 400 man-hours of cutting available each week and 300 man-hours of smoothing. The firm calculates that they can make 3 Euro profit on each rounded lampstand, 4 Euro profit on each angular lampstand and 5 Euro profit on each rectangular lampstand. However, there is an overhead in terms of the manufacturing process which is reflected in flat rate deduction from gross profit of 10% per rectangular lampstand. Demand is also fairly low, given the cost, so that the market can absorb only 100 rectangular lampstands per day. The problem is to maximise profit. Formulate this as a linear programming problem, giving the three steps and state any assumptions made.

This is what I have:

Step 1: Identify decision variables

X1= Number of rounded lampstands to make per week X3= Number of angular lampstands to make per week X3= Number of rectangualr lampstands to make per week

Step 2: Identify restrictions or constraints

x1 greater or equal to 0 x2 greater or equal to 0 x3 greater or equal to 0

limitations: 1x1 + 2x2 + 2x3 less than or equal to 400 3x1 + 1x2 + 2x3 less than or equal to 300

Step 3: Identify Best Criterion Maximise 3x1 + 4x2 + 5x3

Or does 5x3 become 4x3 due to a 10% deduction?

Do I need to add anything or is this answer fine? Also do I need to represent the 10% deduction on here or is it fine?

How do I go about doing this. Any help well appreciated. Do I need to answer this question or just formulate it? Thanks

• You should say how this was not already answered: math.stackexchange.com/questions/1891019/… – DWin Aug 13 '16 at 22:34
• No because this time there is a third variable being used. – John Aug 13 '16 at 23:09