A financial services company processes applications for home mortgages and comme

Question

A financial services company processes applications for home mortgages and commercial loans for its clients. Both types of applications are first reviewed by the screening department. It takes this department 30 minutes to review each home mortgage application and 120 minutes to review each commercial loan application. After the screening, a credit check is performed, which takes 2 hours for each type of application. Finally, the applications are sent to a loan officer for a final evaluation. It takes a loan officer 1.5 hours to review a mortgage application and 2.5 hours to review a commercial loan application. The company also wants to ensure that it processes at least 100 loans and 150 mortgages each week. The company currently employs 15 staff members in the screening department, 25 staff members in the credit check department, and 25 loan officers. Each employee receives the same salary and works 40 hours per week. The company receives $350 for processing each home mortgage application and $450 for processing each commercial loan application. In order for the process to be effective, the company restricts the maximum number of applications (mortgage and loan applications together) to no more than 450 per week.

Based on the information provided and assuming unlimited demand, set up and solve a profit-maximizing linear programming formulation using Excel.

Explanation / Answer

Problem is

Entering =X2=X2, Departing =S5=S5, Key Element = 11

R5R5 (new) =R5=R5(old)

R1R1 (new) =R1=R1 (old) 120R5-120R5 (new)

R2R2 (new) =R2=R2 (old) 120R5-120R5 (new)

R3R3 (new) =R3=R3 (old) 150R5-150R5 (new)

R4R4(new) =R4=R4 (old)

Entering =X1=X1, Departing =S4=S4, Key Element = 11

R4R4 (new) =R4=R4(old)

R1R1 (new) =R1=R1 (old) 30R4-30R4 (new)

R2R2 (new) =R2=R2 (old) 120R4-120R4 (new)

R3R3 (new) =R3=R3 (old) 90R4-90R4 (new)

R5R5(new) =R5=R5 (old)

Since all CjZj0Cj-Zj0,

Optimum Solution is arrived with value of variables as :
X1=150

X2=100

Maximise Z=97500

MAX Z =3 50X1+X1+ 450 X2 Subject to constraints 30 X1+ 120 X2 36000 120 X1+ 120 X2 60000 90 X1+ 150 X2 60000 1 X1+ 0 X2 150 0 X1+ 1 X2 100 and X1,X20

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