Help with Linear Programming, This is confusing for me!Can anyone help explain this.?

The bookholder company manufactors two types of bookcases out of oak and walnut.Model 01 requires 5 board feed of oak and 2 board feed of walnut.Model 02 requires 4 board ft. of oak and 3 board ft of walnut. A profit of $75 is made on each model 01 bookcase and a profit of $125 is made on each model 02 bookcase. The company has a supply of 1000 board ft of oak and 600 board ft of walnut. The company has orders for 40 model 01 bookcases and 50 model 02 bookcases. These orders indicate the minimum number the company must manufacture of each model.


a) write the set of constraints.


b) write the objective function.


c) graph the set of constraints.


d) determine the number of bookcases of each type the company should manufacture in order to maximize profits.


e)determine the maximum profit.

Help with Linear Programming, This is confusing for me!Can anyone help explain this.?
a) you need lots of variables of course. Usually people use x1, x2, x3.... Rename as needed.


Model01 %26gt;= 40


Model02 %26gt;= 50


oak %26lt;= 1000, %26gt;=0


walnut %26lt;= 600, %26gt;=0





b) the obective is what you want to maximize


z = Model01 * 75 + Model02 * 125





c) graphing constraints. You probably just want to graph the 2 woods, so you'll get a box 1000 x 600.





The rest, you should probably learn to do simplex. There's no other way than hammering it out. You can download free Lindo software at


http://www.lindo.com/downloads/


to check your answers if you can figure out the syntax. It certainly won't help you learn simplex though.





Lindo code:


max 75x1 + 125x2


st


x1%26gt;40


x2%26gt;50


x3%26gt;0


x4%26gt;0


x5%26gt;0


x6%26gt;0


5x1-x3=0


2x1-x4=0


4x2-x5=0


3x2-x6=0


x3+x5%26lt;1000


x4+x6%26lt;600





Result:


x1=40


x2=173


Maximal profit = 24625