Suppose your friend is a restaurant chain owner (only 3 units) facing some competitors challenges related to low price, lets call it a price war. Inside his business he knows that there’s no much cost to be cut. But, he thinks that, maybe if he tries harder to find better supplier with low freight and product costs, he could be in a better situation. So, he decided to hire you a recent grad data scientist to figure out how to solve this problem and to build a tool to make your findings to be incorporated in his daily operations. As a Data Scientist you know that this problem could be solved through the use of lpSolve package.

Our goal here is to expand your knowledge to create custom constraints to be used in real business problems.

Answers to the exercises are available here.

**Exercise 1**

We will solve a transportation problem for your friend’s restaurant chain with 2 different products sold from 4 different suppliers. Create a cost vector that model different costs for each combination of restaurant, supplier and product. Use integer random numbers from 0 to 1000 to fill this vector. In order to be reproducible, set seed equals to 1234.

**Exercise 2**

Create the demand constraints. Consider that every restaurant need a specific quantity for each product. Use integer random numbers from 100 to 500 to define minimum quantities to keep the restaurant open without running out of any supplies.

**Exercise 3**

Create the offer constraints. Consider that every supplier can deliver a specific quantity related to each product. Use integer random numbers from 200 to 700 to define maximum quantities that each supplier can deliver.

**Exercise 4**

Prepare the parameter of the `lp()`

function using the variables created above.

**Exercise 5**

Now, solve these problem with these constraints created so far.

**Exercise 6**

We know that some suppliers have minimum order quantities. Create a new set of constraints to represent that. Use integer random numbers from 50 to 70 to define minimum quantities that we can order from each supplier.

**Exercise 7**

Now, solve these problem with these constraints created so far.

**Exercise 8**

We also know that some vehicles have maximum capacity in terms of weight and volume. Create a new set of constraints to represent that. Use integer random numbers from 100 to 500 to define maximum quantities that we can order from each supplier.

**Exercise 9**

Prepare again the `lp()`

function parameters using the variable created above.

**Exercise 10**

Now, solve these problem with all constraints.

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