# Operations research linear model question

1. Sep 23, 2008

### andrassy

1. The problem statement, all variables and given/known dataDean's Furniture Company assembles regular and deluxe kitchen cabinets from precut lumber. The regular cabinets are painted white, and the deluxe are varnished. Both painting and varnishing are carried out in one department. The daily capacity of the assembly department is 200 regular cabinets and 150 deluxe. Varnishing a deluxe unit takes twice as much time as painting a regular one. If the painting/cvarnishing department is dedicated to deluxe units only, it can complete 180 units daily. The company estimates that the revenues per unit for the regular and deluxe cabinets are 100 and 140, respectively. Find the optimal schedule per day.

3. The attempt at a solutionSo I made my objective function Max z = 100x1 + 140x2 where x1 is the number of regular cabinets to produce and x2 is the amount of deluxe. My constrictions, however, I am unsure to model. It appears that x1 <= 200 and x2<=150 but then there is the part about deluxe only can make 180 and it takes twice as long to make a deluxe, neither of which I am sure how to model in the constrictions. Any suggestions?

2. Oct 9, 2011

### Essam

hi Andrassy..
gd evening.. hope u r fine and doing well n ur life..
mmmmm.. i was wondering did u know how 2 solve this problem at the end..?!