## Integer Programming Problem

A machine shop makes two products. Each unit of the first product requires 3 hours on machine 1 and 2 hours on machine 2. Each unit of the second product requirs 2 hours on machine 1 and 3 hours on machine 2. Machine 1 is availbale only 8 hours per day and machine 2 only 7 hours per dau. The profit per unit sold is 16 for the first product and 10 for the second. The amount of each product produced per day must be an integral multiple of 0.25. The objective is to determine the mix of prioduction quanties that will maximise profit.

Q: Formulate an IP model for this problem.

A: My decision varaibles are $\displaystyle x_{1}$=amount of product one to produce and $\displaystyle x_{2}$=amount of product two to produce.

Objective $\displaystyle Z=16x_{1}+10x_{2}$

subject to $\displaystyle 3x_{1}+2x_{2}\leq\\8$
$\displaystyle 2x_{1}+3x_{2}\leq\\7$
and
$\displaystyle x_{1},x_{2}\geq\\0$

with $\displaystyle x_{1},x_{2}$ integer.

I am not sure what to make of the of the last line, "The amount of each product produced per day must be an integral multiple of 0.25." I am not sure what an integral multiple is. I think it is a typo.

I just want to be sure my set up is correct before begin the branch and bound process.

Thanks