Decision Models

1.

1. The LP formulation of the problem where,

Decision Variables:

X1 : Calls made during Daytime

X2 : Calls made during evening

Objective function:

MIN:  3X1 + 5X2   }  Total Cost of calls has to be minimized.

Constraints:

• 0.3X1 + 0.3X2    ≥   600   } Wives contacted
• 0.1X1 + 0.3X2    ≥   480   } Husbands contacted
• 0.1X1 + 0.15X2  ≥   400   } Single Males contacted
• 0.1X1 + 0.2X2    ≥    400  } Single females contacted
• 0.4(X1 +  X2)        ≤      X2      } 40% of total calls can be evening calls.

i.e,  0.4 X1 – 0.6X2  ≤   0 

• X1,X2       ≥  0    } Non negativity conditions

b.) The optimal solution results in a minimum cost value of $12666.67 

[pic 1]   

c.) From sensitivity report below the maximum drop in price without affecting the number of calls during daytime or evening is mentioned in the ‘allowable decrease’ column in the sensitivity report below.

So if daytime calls get cheaper will still not change the number of contacts made during evening.

But if the cost of evening calls drops by more than 0.5, solving the LP leads to a totally different optimal solution showing that there will be no daytime calls. All calls will be made only during evening. This confirms the above sensitivity report.

[pic 2]

2.

1. The LP formulation of the problem where,

Decision Variables:

X1 : White sand from North Dakota

X2 : White sand from Florida

X3 : Raw cotton from North Dakota

X4 : Raw cotton from Alabama

Objective function:

MIN:  0.2X1 + 0.09X2 + 0.05X3 + 0.36X4   } Total Cost of procurement of White sand and cotton has to be minimized.