Our orders are delivered strictly on time without delay 
Question 1
Many times, linear optimization is used to maximize an objective function because profit, productivity, or
efficiency is the outcome of interest. Provide two examples where the goal is to optimize a process by
minimizing an objective function. In your examples, identify the outcome and any constraints that would need
to be met.
Question 2
When many constraints are present in a linear optimization problem, there is a greater chance that a redundant
constraint exists. Assume you are trying to maximize an objective function and you have two decision
variables, X1 and X2. If a redundant constraint exists, does the constraint become necessary if you try to
minimize (instead of maximize) the same objective function? Why? Do you need an objective function to
determine if a constraint is redundant? Explain.
Question 3
Many linear optimization problems can be solved by finding a graphical solution, but there are some problems
that require more advanced spreadsheets and software to find an optimal solution. Describe an optimization
problem in which finding a solution would be impossible using the feasible-region approach. Discuss the
attributes the problem would have to make it impossible to solve using the feasible-region approach.
Question 4
Optimization techniques are used in many applications. For example, when customers order products from an
online store, the shipper has to determine the optimal way to get the product delivered to the customer. The
delivery path that is chosen is the path that minimizes shipping costs while simultaneously satisfying these
constraints:
1. The product must arrive by a promised date.
2. The shipper must deliver a finite set of items.
3. The product must originate from one of several warehouse hubs across the country.
Discuss whether there can be multiple solutions (i.e., more than one path to get the product to your house).
Explain why. Is there a guarantee that a solution always exists? Explain.
