Question

Please hurry only have 30m to answer

A company manufactures a product that is curenty in short supply at ts plants in C and D, then ships the product to ts tour dstituion centers n K. L. M. and N The ransportation costs per unt on collars per un a from C to K, L, M, and N: 16, 10. 15, and 28 ftrom D to K, L, M, and N 8 13, 35, and 16. The monthly demand from K, L. M, and N are: 1900, 00,700, and 1000 unts, respectively Develop a linear programming model that can be used to determine the dstnibution plan that wil minimize total monthly transportation cost On the other hand, the monthly capacity at plants C and D are: 1900 and 2000 units, respectively Use 4 decimal places when necessary and do not use any commas in your answers Fill in the answer to the tollowing questions The solution suggests unts from Cto K units trom C to M units rom C to N units trom D to K units from D toL units from DtoM unts from D TON The total monthly transpornation cost is The distribution center K receives The distribution center L The disinbution center M The distrbution center N

Answer 1

Here Demand >Supply resulting in short-supply to turn into a balanced transportation problem we will add a dummy source with the short supply considering 0 cost of transporting from Dummy Source to destinations

	K	L	M	N	Supply
C	16	10	15	28	1900
D	8	13	35	16	2000
Dummy Source	0	0	0	0	600
Demand	1900	900	700	1000

Let,

Xij = number of units transported from Plat i to Customer location j where i = [C,D and Dummy Source] and j = [K,L,M,N] respectively

Objective is to minimize cost = Min 16x11+10x12+15x13+28x14+8x21+13x22+35x23+16x24+0x31+0x32+0x33+0x34

Subject to,

Supply constraints

x11+x12+x13+x14 <= 1900

x21+x22+x23+x24 <= 2000

x31+x32+x33+x34 <= 600

Demand Constraints (Demand Should be exactly fulfilled so equal sign in the constraint)

x11+x21+x31 = 1900

x12+x22+x32= 900

x13+x23+x33 = 700

x14+x24+x34 =1000

Xij >= 0(Non-negativity constraint)

Solving in excel, we get below transportation schedule:

Send 300 units from C to K

Send 900 units from C to L

Send 700 units from C to M

Send 0 units from C to N

Send 1600 units from D to K

Send 0 units from D to L

Send 0 units from D to M

Send 400 units from D to N

The total monthly transportation cost is $43500

The Distribution centre K receives 1900 units

The Distribution centre L receives 900 units

The Distribution centre M receives 700 units

The Distribution centre N receives 400 units

Solver screenshot

12 x13 x14 x21 (22 x23 124 31 132 133 x34 300 900 1600 600 Objective Function 43500 Constraints 5 Supply constraint 6 Supply constraint D 1900 2000 1900 2000 Supply constraint 7 Dummy Source 600 600 9 Demand of K 10 Demand of L 11 Demand of M 12 Demand of N 13 1900 900 700 1000 1900 900 700 1000

Sensitivity report screenshot

6 Variable Cells Final Reduced Valu Cost Objective Coefficient llov ablelloable Cell Name Increa 16 10 seJecrease 9 $B$3 11 10 $C$3 12 11$D$3 13 12$E$3 14 $F$3 H21 14 $G$3 H22 15 $H$3 k23 16 $I$3 24 17 J$3 31 18 $K$3 H32 19 $L$3 33 20 $M33 34 900 700 111E+30 9 1E+30 28 1E+30 1600 13 1E+30 35 1E+30 28 400 16 0 1E+30 0 1E 0 1E+30 14 +30 14 600 8 1E+30 22 Constraints 23 24 25 $N$5 Supply constraint C 26$N$6 Supply constraint D 27 N$7 Supply constraint Dummy Sourc 600 28 $N$9 Demand of K Final Shado Value Price Constraint R.H. Side llov ablelloable IncreaseJecrease Cell Name 1900 2000 1900 1E+30 300 300 2000 29 N$10 Demand of L 30N$11 Demand of M 31 N$12 Demand of N 1900 900 700 1000 24 16 10 600 1900 900 700 1000 300 900 700 300 24