Motor Startup You are a small car manufacturer with an assembly line in Detroit
ID: 454555 • Letter: M
Question
Motor Startup
You are a small car manufacturer with an assembly line in Detroit and an assembly line in Dallas Your Plant in Detroit has 3 thousand tons of steels available for production until next month. The plant in Detroit is closer to the steel mill, hence you can get them for about $250 per ton. Since it is an older plant, you have more employee at this facility (about 10,000 labor hours are available this month), but they are also paid more ($25 per hour) because they are at the plant for a longer period of time. He energy cost in Detroit is about $5 per kilowatt. You have access to unlimited amount of electricity in Detroit.
Your Dallas plant I newer plant, but it is much further away from the steel mill. You are sourcing the steel for $350 per ton and you have about 2,500 tons of steel available for production until next month. You don’t have as many employees at this facility (about 7,000) labor hours are available this month), but they are paid at $19.50 per hour. The energy cost in Dallas is 40% less than in Detroit. You also have access to unlimited amount of electricity in Dallas.
You are producing two types of vehicles at these two facilities, small truck and sedan. A simplified production requirement for each product are as follows: producing a small truck need 25 labor hours, 3 tons of steels, and 40 kilowatt to manufacture; creating a sedan require 19 labor hours, 2 tons of steels, and 25 kilowatt to manufacture. The requirement is the same for both facilities.
Your major markets are New York City, Charlotte, Orlando, St. Louis, Chicago, Los Angeles, and Seattle. The cost of transportation from each facility is presented below:
Cost per unit shipped to destination:
Detroit Dallas
City
Small Truck
Sedan
Small Truck
Sedan
New York
$100
$90
Charlotte
$150
$120
$200
$150
Orlando
$100
$70
St. Luis
$70
$50
$50
$40
Chicago
$30
$20
Los Angeles
$150
$140
Seattle
$200
$180
Each small truck may be sold for $5,500 while each sedan may be sold for $2,900.
You expect the demand for sedan is about the same across all the city at 60 per city. However, the demand for small trucks is much lower with New York, Chicago, and Seattle each need about 20 trucks per city. Charlotte and St. Louis needs about 25 trucks for each city. Orlando and Los Angeles need only 30 trucks for each city.
Product Mix Question:
Assuming that you can sell everything that you can produce, what should be the production mix for your Detroit and Dallas (without the transportation cost) to minimize your bottom line. Provide the system of linear equations and solve it using Excel Solver. Print out the sensitivity report and discuss (describe the solution.
Would you like to have more labor or more steel? Explain.
Transportation Question:
Suppose you manufacture 150 small truck and 250 sedan from both Detroit and Dallas plant (small trucks and sedan), how should you satisfy the demand from each city to minimize your total cost? Provide the system of linear equations and solve it using Excel Solver. Print out sensitivity report and discuss (describe) the solution. How many small truck and sedan are shipped from Detroit? How many small truck and sedan are shipped from Dallas?
Combined Product Mix and Transportation Question:
Since we live in the “real” world, what is the optimum profit you can generate from this company for this month? Provide the system of linear equations and solve it using Excel Solver. Print out the sensitivity report and discuss (describe) the solution.
A. Identify the most profitable vehicle-route combination. Identify the least profitable vehicle-route combination.
B. Which city generate the highest profit for you?
C. Which city is most unhappy with your service (the city that has the highest unfulfilled order)?
D. Explain, using the sensitivity report, which resource would you want to have more of, steel or labor (identify which facility you want the resource in).
E. If you can produce more sedan or truck, where would you send?
Explanation / Answer
Minimize: Cost
z=x1+x2+x3
Subject to the constaint
250x1 +25x2+5x3<3,000 ton
350x1+19.50x3+2<2,500 ton
x1+x2x+3<0
________________________________
Production requirement
Minimize the production
z=60x1+20x2 +25x3+30x4
Subject to the constaint
25 x1+3 tonsx2+40 x3<10,000
19 x1+2 tonsx2+25x3<7,000
x1,x2,x3<0
________________________________________________
a) most profitable vehicle-route combination is Chicago which is having low transporation cost.
Small Truck $30
Sedan $20
least profitable vehicle-route combination is Seattle which is having higher transporation cost.
Small Truck =$200
Sedan =$180
______________________________________________________________________________
b)Detroit small truck = $250 per ton+$25 per hour+$5 per kilowatt
producing a small truck need 25 labor hours*$25 per hour=$625
3 tons of steels *$250 per ton =$750
40 kilowatt to manufacture * $5 per=$200
=$625+$750+$200
=$1575
Sale - expense
=$5,500- $1575-$30Chicago Trasnporation cost
=$3,895 profit
creating a sedan require 19 labor hours, 2 tons of steels, and 25 kilowatt to manufacture.
producing a sedan need 19 labor hours*$25 per hour=$475
2 tons of steels *$250 per ton =$500
25 kilowatt to manufacture * $5 per=$125
=$475+$500+$125
=$1,100
Sale - expense
$2,900 -$1,100 -$20Chicago Trasnporation cost
=$1,780
______________________________________________________________________
Dallas
$350 per ton+$19.50 + 2(40%of 5=2)
producing a small truck need 25 labor hours*$19.50 per hour=$487.50
3 tons of steels *$350 per ton =$1050
40 kilowatt to manufacture * $2 per=$80
=$487.50+$80+$1050
=$1,617.50
$5,500-$1,617.50-$30Chicago Trasnporation cost
=$3852.50 profit
producing a sedan need 19 labor hours*$25 per hour=$475
2 tons of steels *$250 per ton =$500
25 kilowatt to manufacture * $5 per=$125
=$475+$500+$125
=$1100
Sales- Expenses=profit
$2,900- $1100-$20Chicago Trasnporation cost
=$1,780
chicago will bring higher profit at same time small truck brings more profit for all cities.
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