# Linear Programming model

• Nov 25th 2007, 02:42 AM
Juggler
Linear Programming model
I was having a problem developing the optimal solution. I tried to find the objective function, and decision variables/constraints but I got confused. Any pointers would be appreciated. Thanks.

Tots Toys makes a plastic tricycle that is composed of three major components: a handlebar-front wheel-pedal assembly, a seat and frame unit, and rear wheels. The company has orders for 12,000 of these trikes.

As indicated in the table below, the company obviously does not have the resources available to manufacture everything needed for the completion of 12000 tricycles, so it has arranged to purchase additional components, as necessary. Develop a linear programming model to tell the company how many of each component should be manufactured and how many should be purchased in order to provide 12000 fully completed tricycles at the minimum cost.

http://img100.imageshack.us/img100/918/50876770es7.png
• Nov 27th 2007, 03:07 PM
Let $\displaystyle F_p$, and $\displaystyle F_m$ refer to front parts manufactured and produced... Similarly $\displaystyle S_p, S_m$ refers to seat, and $\displaystyle W_p, W_m$ refers to rear wheels.

We wish to minimize the cost:

$\displaystyle \text{Cost} = 12F_p + 8F_m + 9S_p + 6S_m + 3W_p + W_m$

given the following constraints:

we want 12000 parts, and 24000 rear wheels:
$\displaystyle F_p + F_m = 12000, S_p + S_m = 12000, W_p + W_m = 24000$

and we have limited parts/time/space available so:
$\displaystyle 3F_m+4S_m + 5W_m \leq 50000$

$\displaystyle 10F_m + 6S_m + 2W_m \leq 160000$

$\displaystyle 2F_m + 2S_m + W_m \leq 30000$

then one would use some magical linear programming techniques to find the optimal values for $\displaystyle F_m, F_p, S_m, S_p, W_m, W_p$