Please formulate and solve each of the following problems. For each problem, you should include the...

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Advance Math

Please formulate and solve each of the followingproblems. For each problem, you should include the finalSOLVER printout (either your final spreadsheet oran answer report), as well as (1) clear and precise definitions forall decision variable; (2) your objective function indicatingwhether it is to be maximized and minimized; (3) all constraints,including non-negativity and integrality (if necessary); and (4)what the optimal decision is (in words) and what outcome will beproduced.
A manufacturer of stereos has plants in Atlanta, New Haven andDallas, and distributions centers in San Francisco, Boston,Washington, D.C., and Cleveland. The tables show weekly productioncapacities, demand requirements, and unit transportation costs (indollars).
ORIGIN
PRODUCTION
DESTINATION
REQUIREMENTS
Atlanta
65
San Francisco
50
New Haven
75
Boston
35
Dallas
45
Washington, D.C.
35
Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â ClevelandÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 65
UNIT TRANSPORTATION COSTS
San Francisco
Boston
Washington, D.C.
Cleveland
Atlanta
13
9
6
5
New Haven
11
6
7
4
Dallas
7
8
15
10
The goal is to minimize totaltransportation costs.
3. A company has five jobs, each of which must be assigned to asingle machine. The table shows the dollar costs for each possiblejob-machine assignment:
JOBÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â MACHINE
Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â AÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â BÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â CÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â DÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â E
1Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 138Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 127Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 118Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 121Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 143
2Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 157Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 138Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 129Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 132Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 160
3Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 143Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 129Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 131Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 130Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 172
4Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 111Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 119Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 123Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 107Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 120
5Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 102Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 120Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 100Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 119Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 100Â Â Â Â Â
Find the set of assignments with thelowest possible total cost.

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4.1 Ratings (706 Votes)

We will be using LINGO OPTIMIZATION TOOL to solve the above problems The transportation cost matrix is as follows SAN FRANSISCO BOSTON WASHINGTON DC CLEVELAND ORIGIN ATLANTA 13 9 6 5 65 NEW HEAVEN 11 6 7 4 75 DALLAS 7 8 15 10 45 DESTINATION 50 35 35 65 Summation of ORIGIN Summation of DESTINATION 185 Therefore this transportation problem is balanced Our objective is the minimization of TRANSPORTATION COST VARIABLES DECLARATION x11 Number of units from Atlanta to San Fransisco x12 Number of units from Atlanta to Boston x13 Number of units from Atlanta to Washington DC x14 Number of units from Atlanta to Cleveland x21 Number of units from New Haven to San Fransisco x22 Number of units from New Haven to Boston x23 Number of units from New Haven to Washington DC x24 Number of units from New Haven to Cleveland x31 Number of units from Dallas to San Fransisco x32 Number of units from Dallas to See Answer

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ORIGIN	PRODUCTION	DESTINATION	REQUIREMENTS
Atlanta	65	San Francisco	50
New Haven	75	Boston	35
Dallas	45	Washington, D.C.	35

UNIT TRANSPORTATION COSTS
	San Francisco	Boston	Washington, D.C.	Cleveland
Atlanta	13	9	6	5
New Haven	11	6	7	4
Dallas	7	8	15	10