6. The Charm City Company has four plants to produce HDTVs. These plants ship HD

Question

6. The Charm City Company has four plants to produce HDTVs. These plants ship HDTVs to three markets. The following table summarizes the sh at each plant, and the weekly demand at each market. from a plant to a market,the weekdy production s (in dollars) from a plant to a at weekly demand aring nastk Market 1 Market 2 Market 3 Production Plant 1 Plant 2 Plant 3 Plant 4 10.1 8.2 9.4 9.4 8.5 7.8 9.6 9.6 12.0 10.3 9.7 9.7 650 680 575 525 Demand 1000 950 450 The management wants to ship at least 500 HDTVs from Plant 3 to Market 1. They do not want to ship any HDTVs from Plant 1 to Market 2 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 Note: Do NOT solve the problem after formulating.

Explanation / Answer

Objective Function is Minimizing the Shipping cost while Meeting all the constraint of each market.

Min: 10.1*P1M1+ 8.5*P1M2+ 12*P1M3+ 8.2*P2M1+7.8*P2M2+ 10.3*P2M3+ 9.4*P3M1+9.6*P3M2+9.7*P3M3+ 9.4*P4M1+9.6*P4M2+ 9.7*P4M3

S.T.

P1M1+ P1M2+ P1M3<=650

P2M1+P2M2+ P2M3<=680

P3M1+P3M2+P3M3<=575

P4M1+P4M2+ P4M3<=525

P1M1+P2M1+P3M1+P4M1<= 1000

P1M2+P2M2+P3M2+P4M2<= 950

P1M3+P2M3+P3M3+P4M3<= 450

P3M1>=500

P1M2=0

PiMj.>=0, i=1,4, j=1,3

Market 1 Market 2 Market 3 Production Plant 1 10.1 8.5 12 650 Plant 2 8.2 7.8 10.3 680 Plant 3 9.4 9.6 9.7 575 Plant 4 9.4 9.6 9.7 525 Demand 1000 950 450 Decision Varible that shows Quantity Supplied From Plant to Market Market 1 Market 2 Market 3 Production Plant 1 P1M1 P1M2 P1M3 P1M1+ P1M2+ P1M3 Plant 2 P2M1 P2M2 P2M3 P2M1+P2M2+ P2M3 Plant 3 P3M1 P3M2 P3M3 P3M1+P3M2+P3M3 Plant 4 P4M1 P4M2 P4M3 P4M1+P4M2+ P4M3 Demand P1M1+
P2M1+
P3M1+
P4M1 P1M2+
P2M2+
P3M2+
P4M2 P1M3+
P2M3+
P3M3+
P4M3

Related Questions

Navigate

• Browse (All)
• Browse 6
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.