Question $15$ to Question $17$ is based on this problem. A company has three warehouses that supply four stores with a given product. Each warehouse has $30$ units of the product. Stores $1,2,3,$ and $4$ require $20,25,30$ and $35$ units of the product, respectively. The per unit shipping costs from each warehouse to each store are given in the following table: Table $7-$ Exam $2-1.$png Note that all the demands from the four stores will not be fulfilled completely, because the total demand exceeds the total supply. Let Xij be the units of the product to be shipped from warehouse i to store j$.$ Create a spreadsheet for this problem and solve it by Solver. Without including the nonnegativity constraints, how many constraints in total do we need for the LP formulation of this problem?

A railroad needs to move the maximum amount of material through its rail network. The

numbers on arcs represent maximum flow. Formulate the LP model to determine this

maximum amount based on the following network diagram.

Let Xij be the amount of material flowing from node i to node $j.$

What is the objective function in the maximal flow problem depicted in the above diagram?

Max X$61$

Max X$13+$ X$35+$ X$34+$ X$46$

Max X$12+$ X$25+$ X$56$

Max$13$

Max X$12$