Problem 2
Vehicles
Cars
Trucks
SUVs Steel Req’d per vehicle MPG
1
3
2 Inventory
Cars
Trucks
SUVs Month 1 Demands
Cars
Trucks
SUVs Month 1 20
10
17 200
100
50 Month 2
600
200
400 300
300
200 Questions
1 – Write out your logic for the objective function for Problem 2. For this, you may use an algebraic statement, or you may write
2 – Describe all constraints in Problem 2. For this, you may use algebraic statements, or you may write it out in words.
3 – Based on the result of your optimization for Problem 2, what is the total cost (of production and inventory) over the two mo
4 – Questions in this section will require you to alter the results in your model to test calculations. To do this, Save a Copy of you
4a – Modify your Problem 2 model to show production of 10 vehicles of each type, each month. What is the Total Cost of Mate
4b – Modify your Problem 2: Production Planning model to show production of 10 vehicles of each type, each month. What is t Steel Cost
Month 1
Month 2
$
700 $
800 Holding Cost
per vehicle
$ 200 Avg MPG per Production Cycle
Minimum MPG
16 An automobile manufacturer makes three types of vehicles: Cars, Tru
Each Car produced requires 1 ton of steel and gets 20 miles per gallon
Truck requires 3 tons of steel and gets 10 mpg. Each SUV requires 2 to
gets 17 mpg. The manufacturer must determine a production plan for these three t
for each of the next two months. In Month 1, steel is expected to cost
Month 2, steel is expected to cost $800. Steel must be used in the mo
purchased. A maximum of 2500 tons of steel is available for purchase At the beginning of Month 1 there 200 Cars, 100 Trucks and 50 SUVs i
Month 1, there is a demand for 600 Cars, 200 Trucks and 400 SUVs. A
unsold in Month 1 may be used to meet demand in Month 2. Any veh
after meeting demand in Month 1 will be held in inventory at a cost o
vehicle. In Month 2, there is a demand for 300 Cars, 300 Trucks, and 2
maximum of 1000 vehicles may be produced in a single month. Industry standards require that the average gas mileage of all vehicles
given month should be at least 16 mpg. Build a linear programming model to determine how to minimize the
(production + inventory cost) while meeting demands, and staying wi
requirements of available material (steel), production limits, and a ga
considerations. statement, or you may write it out in words. Describe the overall goal for the objective.
rite it out in words.
d inventory) over the two months, according to the optimal solution? Enter your exact answer.
To do this, Save a Copy of your Excel file. In the copy, change the values of each of your decision variables to 10. Answer the questions in th
hat is the Total Cost of Material (steel) under this condition? Enter your answer with 2 decimal places
type, each month. What is the Total Cost of Inventory under this condition? Enter your answer with 2 decimal places. (Note that this will li e types of vehicles: Cars, Trucks, and SUVs.
and gets 20 miles per gallon (MPG). Each
mpg. Each SUV requires 2 tons of steel and duction plan for these three types of vehicles
th 1, steel is expected to cost $700 per ton. In
Steel must be used in the month is is
teel is available for purchase each month. ars, 100 Trucks and 50 SUVs in inventory. In
200 Trucks and 400 SUVs. Any vehicles
demand in Month 2. Any vehicles remaining
held in inventory at a cost of $200 per
r 300 Cars, 300 Trucks, and 200 SUVs. A
ced in a single month. ge gas mileage of all vehicles produced in a ermine how to minimize the total cost
ting demands, and staying within the
, production limits, and a gas mileage 0. Answer the questions in this section based on the results in the copy of your file showing 10 each for the decision variables. This will allo
places. (Note that this will likely be an unrealistic value, given the production quantities are not sufficient to meet demand.) he decision variables. This will allow us to test the outcomes of your calculations and the logic of the model, regardless of the optimal soluti t to meet demand.) egardless of the optimal solution that you reached.
