# Math Help - Help with Linear programming problem

1. ## Help with Linear programming problem

There are three types of machines that can be used to make a chemical. The chemical can be manufactured at four different purity levels. Here is the data.

Machine Capacity: production per day
Production per day if used to manufacture purity
1 2 3 4
1 50 tons $900 1000 1250 1500 2 40 tons 600 750 1000 1050 3 25 tons 400 700 800 900 Monthly demand for chemical at purity level (tons) 150 300 90 175 Penalty per ton short 40 60 75 90 The chemical is used by the company internally; if the company does not manufacture enough of It, It can be bought at a price, which is called the penalty for shortage. Assume that there are 30 production days per month at the company. Formulate the problem of minimizing the overall cost as an LP. Can anyone help me find the Variables, Constraints and the objective?? 2. Originally Posted by Maxerazzi There are three types of machines that can be used to make a chemical. The chemical can be manufactured at four different purity levels. Here is the data. Machine Capacity: production per day Production per day if used to manufacture purity 1 2 3 4 1 50 tons$900 1000 1250 1500
2 40 tons 600 750 1000 1050
3 25 tons 400 700 800 900

Monthly demand for chemical at
purity level (tons) 150 300 90 175
Penalty per ton short 40 60 75 90

The chemical is used by the company internally; if the company does not manufacture enough of It, It can be bought at a price, which is called the penalty for shortage. Assume that there are 30 production days per month at the company. Formulate the problem of minimizing the overall cost as an LP.

Can anyone help me find the Variables, Constraints and the objective??
The variables are $X_{i,j}$ the number of days production by machine $i$ of quality level $j$.

With these variables tables give the constraints. The objective is the total cost of meeting the production quotas when the penalty costs for the short fall in company production is included.

CB

3. Well my Lp isn't that great, this is what i originally had as an answer:

Variables: purity=P, machine=M

P1M1, P1M2, P1M3
P2M1, P2M2, P2M3
P3M1, P3M2, P3M3
P4M1, P4M2, P4M3

Objective:

MINIMIZE; 900 P1M1 + 1000 P2M1 + 1250 P3M1
+ 1500 P4M1 + 600 P1M2 + ......... 900 P4M3.

Constraints:

demand purity level;

Demand1 : P1M1+P1M2+P1M3 >= 150
D2 : P2M1+P2M2+P2M3 >= 300
D3 : P3M1+P3M2+P3M3 >= 90
D4 : P4M1+P4M2+P4M3 >= 175

This is what I had so far. Is some correct or is it totally wrong?