b.
Solve the model you developed in part (a).
c.
How much may the yields on the three funds vary before it will be necessary for Pfeiffer to
modify Hartmann’s portfolio?

d.
If Hartmann were more risk tolerant, how much of a yield increase could he expect? For
instance, what if his portfolio risk index is increased to 0.06?

e.
If Pfeiffer revised the yield estimate for the growth fund downward to 0.10, how would you
recommend modifying Hartmann’s portfolio?

Chapter 9
Problem 2 (8 points)
The management of Hartman Company is trying to determine the amount of each of two products to
produce over the coming planning period. The following information concerns labor availability, labor
utilization, and product profitability:
a.
Develop a linear programming model of the Hartman Company problem. Solve the model to
determine the optimal production quantities of products 1 and 2.

Y = units of production 2 produced
Max 30x + 15Y
X + 0.35y <=100
0.3X + 0.2Y <= 36
0.2X + 0.5Y <= 50
X,Y >= 0
X + 0.35y <=100
X = 100
Y = 285.71
0.3X + 0.2Y <= 36
X = 120
Y = 180
0.2X + 0.5Y <= 50
X = 250
Y = 100
Max = 30x + 15Y
30(
77.894)
+ 15(
63.157)
=2,336.84 + 947.355
= 3284.20
b.
In computing the profit contribution per unit, management doesn’t deduct labor costs because
they are considered fixed for the upcoming planning period. However, sup pose that overtime
can be scheduled in some of the departments. Which departments would you recommend
scheduling for overtime? How much would you be willing to pay per hour of overtime in each
department?
X + 0.35y <=100
0.3X + 0.2Y <= 36 (3.33)
X + 2/3y = 120
Y = 63.157
X + 0.35 = 100
X + 0.35(=63.15789) = 100
X + 22.10526 = 100
X = 77.894
Optimal(77.894, 63.157)