# Linear Programming model

• November 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
• November 27th 2007, 03:07 PM
Let $F_p$, and $F_m$ refer to front parts manufactured and produced... Similarly $S_p, S_m$ refers to seat, and $W_p, W_m$ refers to rear wheels.

We wish to minimize the cost:

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

given the following constraints:

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

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

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

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

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