# Gurobi/Example

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We are using the example from the gurobi website

```http://www.gurobi.com/documentation/7.0/quickstart_linux/solving_a_simple_model_the.html
```

to demonstrate how to solve a simple model.

Imagine that it is the end of the calendar year at the United States Mint. The Mint keeps an inventory of the various minerals used to produce the coins that are put into circulation, and it wants to use up the minerals on hand before retooling for next year's coins.

The Mint produces several different types of coins, each with a different composition. The table below shows the make-up of each coin type (as reported in the US Mint coin specifications).

``` 	        Penny	Nickel	Dime	Quarter	Dollar
Copper (Cu)	0.06g	3.8g	2.1g	5.2g	7.2g
Nickel (Ni)	 	1.2g	0.2g	0.5g	0.2g
Zinc (Zi)	2.4g	 	 	 	0.5g
Manganese (Mn)	 	 	 	 	0.3g
```

Suppose the Mint wants to use the available materials to produce coins with the maximum total dollar value. Which coins should they produce?

The corresponding gurobi input file looks like

```[leonhard@eu-login-10 ~]\$ cat coins.lp
Maximize
.01 Pennies + .05 Nickels + .1 Dimes + .25 Quarters + 1 Dollars
Subject To
Copper: .06 Pennies + 3.8 Nickels + 2.1 Dimes + 5.2 Quarters + 7.2 Dollars -
Cu = 0
Nickel: 1.2 Nickels + .2 Dimes + .5 Quarters + .2 Dollars -
Ni = 0
Zinc: 2.4 Pennies + .5 Dollars - Zi = 0
Manganese: .3 Dollars - Mn = 0
Bounds
Cu <= 1000
Ni <= 50
Zi <= 50
Mn <= 50
Integers
Pennies Nickels Dimes Quarters Dollars
End
```

The job is then submitted using the gurobi command line interface:

```[leonhard@eu-login-10 ~]\$ bsub -n 1 -W 0:10 -R "rusage[mem=512]" "gurobi_cl ResultFile=coins.sol coins.lp"
Generic job.
Job <60506881> is submitted to queue <normal.4h>.
JOBID      USER        STAT  QUEUE      FROM_HOST   EXEC_HOST   JOB_NAME   SUBMIT_TIME
60506881   Leonhard    PEND  normal.4h  eu-login-10             * coins.lp Apr  4 13:21
JOBID      USER        STAT  QUEUE      FROM_HOST   EXEC_HOST   JOB_NAME   SUBMIT_TIME
60506881   Leonhard    RUN  normal.4h   eu-login-10 eu-ms-013-0 * coins.lp Apr  4 13:21
No unfinished job found
```

The solution is then written to the file coins.sol:

```[leonhard@eu-login-10 ~]\$ cat coins.sol
# Objective value = 113.45
Pennies 0
Nickels 0
Dimes 2
Quarters 53
Dollars 100
Cu 999.8
Ni 46.9
Zi 50
Mn 30