decision variable, objective function, constraint

Question

The Charm City Company has three plants to produce HDTVs. These plants ship HDTVs to four markets. The following table summarizes the shipping costs (in dollars) from a plant to a market, the weekly production at each plant, and the weekly demand at each market.

             Market 1     Market 2      Market 3      Market 4       Production
__________________________________________________________________
Plant 1    10.1              8.5             12.0             14.2              600
Plant 2     8.2              7.8              10.3             13.5              620
Plant 3     9.4              9.6               9.7              12.6              580
__________________________________________________________________
Demand    500            700            350               250

The management wants to ship at least 300 HDTVs from Plant 3 to Market 2. They do not want to ship any HDTVs from Plant 2 to Market 4 because of possible shipment delays.

Formulate a linear programming model to minimize the total cost of shipping for this transportation problem.

(a) Define the decision variables.
(b) Determine the objective function. What does it represent?
(c) Determine all the constraints. Briefly describe what each constraint represents.

Answer 1

Manaal,

 

This problem has twelve decision variables, showing how many tv's are shipped from each of the three plants to the four markets. Call shipping units for plant one X1,x2,x3,x4; shipping units for plant two y1, y2, y3, y4; and finally shipping units for plant three z1,z2,z3,z4.

 

The objective is to minimize shipping cots so that would be 

10.1x1+8.5x2+12x3+14x4.....+9.4z1+9.6z2+9.7z3+126z4

 

The first  set of constraints for transportation is supply (production) and demand.

Supply: at most here.

X1+x2+x3+x4<=600

Y1+y2+y3+y4<=620

Z1+z2+z3+z4<=580

And demand for each of themarkets: at least here.

X1+y1+z1>=500

X2+y2+z2>=700

X3+y3+z3>=350

X4+y4+z4>=250

 

At least 300 tc's from plant three to market 2: z2>=300

No tv's from plant two to market four: y4=0

 

You can use excel solver to minimize the  objective function. just don't include that last variable as a decision variable in excel so as to force it to 0.

 

Hope that helps,

Deanna