Question

1. The Primo mortgages. The Insurance Company is introducing two new product lines: special risk insurance and expected profit is S5 per unit on special risk insurance and $2 per unit on mortgages. nagement wishes to establish sales quotas for the new product lines to maximize total expected profit The work requirements are as follows: 

Define the decision variables and formulate a linear programming model for this problem. (20 scores) 

2. The board of directors of General Wheels Co. is considering six large capital investments. Each investment can be made only once. These investments differ in the estimated long-run profit (net present value) that they will generate as well as in the amount or capital required, as shown by the following table (in units of millions of dollars). 

The total amount of capital available for these investments is $100 million. Investment opportunities 1 and 2 are mutually exclusive, and so are 3 and 4. Furthermore, neither 3 nor 4 can be undertaken unless one of the first two opportunities is undertaken. There are no such restrictions on investment opportunities 5 and 6. The objective is to select the combination of capital investments that will maximize the total estimated long-rm profit (net present value). 

Define the decision variables and formulate a 0-1 integer programming for this problem.

Answer 1

1.

Let's Assume Primo Insurance Company sell "X" units of special risk insurance and "Y" units of mortgages.

Constraint matrix is as below -

Department	Works hours per unit		Works are available
	Special risk insurance	Mortgages
Underwriting	3	2	2400
Administration	0	1	800
Claims	2	0	1200

This table implies that, Underwriting department has maximum 2400 hrs available and any sale quantity combination of special risk insurance and mortgages could not have more than 2400 hrs of underwriting department. Similarly, Administration has maximum 800 hrs available and Claims has maximum 1200 hrs available.

Further, Underwriting requires 3 hours for Special risk insurance and 2 hours for Mortgages , Administration requires 0 hours for special risk insurance and 1 hour for mortgages and Claims requires 2 hours for special risk insurance and 0 hours of Mortgages.

Decision Variable are unknown values and which values are required by management in such manner so that it maximize the result or objective.

In our case, Decision variables are sale units of special risk insurance "X" and sale units of mortgages "Y"

Formulation of a linear programming model for this problem

The expected Profit of special risk insurance is $ 5 and mortgages is $ 2

Lets say "Z" is objective of Primo Insurance company , which to maximize profit of company.

Thus, Objective Function would be -

Z = 5X + 2Y

and constraints would be -

3X + 2Y $\leq$ 2400

Y $\leq$ 800

2X $\leq$ 1200

X,Y $\geq$ 0