# MGOC10H3 Lecture Notes - Lecture 6: Linear Programming Relaxation, Sensitivity Analysis, Linear Programming

## Document Summary

Pure integer programming (ip) problems all variables have to be integer. Mixed ip problems some variables integer others can be non-integer. Capital budgeting example - abc manufacturing co. (example of binary variables) Abc manufacturing co is considering in setting up 4 production lines with following net present value (npv) payoff and upfront cash investment. It cannot setup eg. three line 1, only one can be setup for each line. Abc has ,000 is available cash at present. Formulate an ip whose solution will tell abc which lines it should set up to maximize npv. Fix cost / setup cost and either-or-constraint example clothing company. A clothing company can manufacture 3 types of clothing: shirts, shorts and pants. The company has the equipment to make pants but will need to rent machinery to make shirts and shorts. The production process for making pants is such that either 0 or at least 10 of them must be made.