Solution: where you may assume that other constraints force 0 - #80186
Problem 1: Consider adding a constraint to a linear program of the form \(\frac{1}{100}{{x}^{2}}+5x-3\ge 0\)
where you may assume that other constraints force 0 ≤ x ≤ 5. You cannot add the constraint as given (Why?) in LINDO so what should you do (using UNDO)? Make suggestions and comment.
Problem 2: (Piecewise Linear Functions) Consider the hiring/firing model. Indicate how to add the constraint that you can fire as many workers as you want in a month but the cost increases with a cost of $420 for first 10, $600 for next 20 and $2000 for any workers beyond 30 in a given month. Add this to the existing model and solve (both obtaining a fractional solution and also the integer solution and then comparing the two objective functions).
Problem 3: (Branch and Bound) Use our branch and bound procedure to solve the following LP where
LP = max 3x1 +6x2 +25x3 +60x4 = z .
24x1 +76x2 +43x3 +754x4 < 860 - n
755x1 +27x2 +33x3 +67x4 < 860 - n
x1 < 1x2< 1
x3<1
x4< 1
where n is the number formed from the last two digits of your student number.
Consider the ILP (Integer Linear Program) obtained from the above LP by adding the constraints that all the variables are 0 or 1. Use Branch and Bound to solve. You may make your own choices which variables to branch on. Record for each LP solved the value for z, the solution and as well as the extra constraints you have added to the LP which determine the current LP. Obtain a Branch and Bound tree as given in the handout with the actual solutions recorded.
Now obtain a solution to the ILP above by using LINDO with the GIN command (INT will also work). Obviously the final answer, at least its z values should agree with what you obtained by using Branch and Bound. Record number of iterations. You might also try to figure out what LINDO is doing (it appears to be our branch and bound with something else I don't understand!).
Deliverable: Word Document
and pdf
