Quantitative Methods

Assessment $2$

a$)$ Write out the model for the following transportation problem $-$ i$.$e$.$ define the variables and state the objective function and constraints.

b$)$ Use Excel Solver to solve the following transportation problem.

The Jessie Cohen Clothing Group owns factories in three towns $(W,x$ and $Y)$ which distribute to three Cohen retail dress shops $($in A$,$ B$,$ and C$).$ Factory availabilities, projected store demands, and unit shipping costs are summarized in the table that follows:

$\backslash$table$[[\backslash$table$[[$FROM$]],$A$,$B$,$C$,\backslash$table$[[$FACTORY$],[$AVAILABILITY$]]],[$w$,|$$$4|,|$$$3|,$$$3,35],[x,|$$$6|,$$$7,$$$6,50],[Y,$$$8,$$$2,$$$5,50],[\backslash$table$[[$STORE$],[$DEMAND$]],|30|,|65|,40,135]]$

a$)$ Write out the model and then

b$)$ Use Excel Solver to solve the following assignment problem:

The Dubuque Sackers, a class D baseball team, face a tough $4$ game road trip against league rivals Des Moines, Davenport, Omaha and Peoria. Manager "Red" Revelle faces the task of scheduling his four starting pitchers for appropriate games. Because the games are to be played back to back in less than one week, Revelle cannot count on any pitcher to start in more than one game.

Revelle knows the strengths and weaknesses not only of his pitchers, but also of his opponents. He has developed a performance rating for each of his starting pitchers against each of these teams. The ratings are listed in the table below.

What pitching rotation should manager Revelle set to provide the highest total of the performance ratings?

$\backslash$table$[[$performance ratings?,,,,$],[,$Opponent$],[$Starting Piteher,Des Moines,Davenport,Omaha,Peoria$],[$Jones$,0\mathrm{.}6,0\mathrm{.}8,0\mathrm{.}5,0\mathrm{.}4],[$Baker$,0\mathrm{.}7,0\mathrm{.}4,0\mathrm{.}8,0\mathrm{.}3],[$Parker$,0\mathrm{.}9,0\mathrm{.}8,0\mathrm{.}7,0\mathrm{.}8],[$Wilson$,0\mathrm{.}5,0\mathrm{.}3,0\mathrm{.}4,0\mathrm{.}2]]$