TITLE: Integer Programming Problem - Machines To Products
QUESTION [0 upvotes]: A man is trying to decide how he can assign his five machines to
four products in order to maximize output. The estimated output per
day for each machine is shown and reflect its productivity for each product. 
At least one machine has to be allocated to each
product and that a machine can be part-allocated to more than one product.
M=MACHINE
P = PRODUCTS 
And P1,P2,P3,P4 in that order
M1: € 500, € 1,010, € 500, € 1,300
M2: € 860, € 1,205, € 310, € 940
M3: € 1,350, € 1,105, € 326, € 500
M4: € 990, € 920, € 490, € 605
M5: € 500, € 1,400, € 495, € 750
I think this is an integer LP problem so that objective function would be BijXij
where i = machines and j = products so what I have so far is that xij is either 1 (for yes) and 0 (for no). 
How would you write the constraints? And is my objective function or understanding on the write path?

REPLY [0 votes]: You are on the right track.
Let $x_{ij}$ be the the boolean variable equal to one if and only if product $j\in P$ is assigned to machine $i\in M$.
Maximize $\sum_{i \in M}\sum_{ j \in P}c_{ij}x_{ij}$ where $c_{ij}$ is the output of product $j$ on machine $i$.
Your only constraint is that at least one machine has to be allocated to each each product:
$$\sum_{i \in M}x_{ij}\ge 1\quad \forall j \in P$$
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