Problem $15-11($Algo$)$

DM Office Products $($DMOP$)$ is a wholesale supplier of office products with one facility in Pennsylvania. It has decided to build a new distribution warehouse in the state of New York to help serve the growing demand in that market. It has four major customers located in Buffalo, Syracuse, Albany. and New York City. Though New York City is the largest market, It also has the greatest competition, and DMOP is not a major player there. When DMOP ships an order to a customer, It uses its own small fleet of two trucks to dellver, so the cost of delvery is essentially the same for a full or partally full truck. The expected number of annual shipments to each city and their coordinates on an $x,y$ grid is shown in the following table:

$\backslash$table$[[$CITY$,x-$COORDINATES,$y-$COORDINATES,NUMBER OF SHIPMENTS$],[$Buffalo$,365,890,95],[$Syracuse$,1,460,940,99],[$Albany$,2,340,670,139],[$New York City,$2,315,20,79]]$

Use the centrold method to recommend a location for the new warehouse for DMOP.

Note: Round your answers to $1$ decimal place.

Bindley Corporation has a one$-$year contract to supply motors for all washing machines produced by Rinso Limited. Rinso manufactures the washers at four locations around the country. New York City, Fort Worth, San Diego, and Minneapolis. Plans call for the following numbers of washing machines to be produced at each location:

$\backslash$table$[[$New York City,$30,000],[$Fort worth,$55,000],[$San Diego,$65,000],[$Minneapolis$,65,000]]$

Bindley has three plants that can produce the motors. The plants and production capacities are

$\backslash$table$[[$Boulder$,100,000],[$Macon$,120,000],[$Gary$,90,000]]$

Due to varying production and transportation costs, the profit Bindley earns on each $1,000$ units depends on where they were produced and where they were shipped. The following table gives the accounting department estimates of the dollar profit per unit. $($Shipment will be made in lots of $1,000)$

$\backslash$table$[[$SRODUCED AT$,$SHIPPED TO$],[$NEW YORK CITY,FORT WORTH,SAN DIEGO,MINNEAPOLIS$],[10,13,15,12],[22,25,22,16]]$

Given profit maximization as a criterion, Bindley would like to determine how many motors should be produced at each plant and how many motors should be shipped from each plant to each destination.

a$.$ Develop a transportation grid for this problem.

$\backslash$table$[[$From$/$To$,$New York City,Fort Worth,San Diego,Minneapolis,Supply$],[$Boulder$,,,,,],[$Macon$,,,,,],[$Gary$,,,,,],[$Requirements$,,,,,]]$

b$.$ Find the optimal solution using Microsoft Excel.

Note: Leave no cells blank $-$ be certain to enter $"0"$ wherever required.

$\backslash$table$[[$Profit$,,,,],[$Boulder$,,,,,],[$Macon$,,,,,]]$