To solve a complex problem, we identify the problem statement (desired variable) and the boundaries (conditions) existing and build a mathematical equation (model) depending on how they affect the desired variable.
Here, Profit is the desired variable being discussed about that is C.
Generally, we try to attain maximum profits. So, we are trying to attain Cmaximum.
For 1 unit of label X1 shipped, profit = C1
For 10 units of label X1 shipped, profit = 10*C1
where Yi is the number of goods labelled Xi being shipped.
Here, we have the boundary or limit related to total resources.
For 1 unit of label X1 shipped, resources utilized = Aj1
For 10 units of label X1 shipped, resources utilized = 10*Aj1
Total number of resources utilized = Aj1Y1+Aj2.Y2+….+AjnYn
The total resources available = Bm
So, if we can utilize more resources, we can ship more items there by attaining more profits. So, we should utilize resources to the maximum i.e.; Bm
Therefore, Bm = Aj1Y1+Aj2.Y2+….+AjnYn
The equations deduced are
1. – Containing the decision variable C
2. Bm = (Aj1Y1+Aj2.Y2+….+AjnYn ) – The condition or limiter
So, if we are given the total resources available and the resource utilized per item, we can solve the problem.
It ccan be done in Excel using solver.
C is target cell (maximum)
Bm – constraint
Yi – cells to be changed