b. Now suppose the manager can invest in any of the five securities but
cares only about the risk constraint. Determine the optimal portfolio.
c. Answer part (b), assuming the manager cares only about the maturity
constraints.- A soft-drink producer must decide how to divide its spending between
two forms of media: television advertising and magazine advertising.
Each 30-second commercial on prime-time network television costs
$120,000 and, by the company’s estimate, will reach 10,000 viewers, 5,000
of whom are in the prime consumer age group, 15 to 25. A single-page
ad in a leading human interest weekly magazine costs $40,000 and
reaches 5,000 individuals, 1,000 of whom are in the 15 to 25 age group.
In addition, the company plans to hold a sweepstakes contest to promote
its new soft drink. (A requirement for entry is to enclose the coded label
from the new drink.) The company believes the print ad will be more
effective in generating trial purchases and entries. Each magazine spot is
expected to produce 500 entries and each television spot 250 entries.
Finally, the company’s goal in its promotion campaign is to reach at least
600,000 total viewers and 150,000 young viewers and to produce 30,000
or more contest entrants.
How many spots of each kind should it purchase to meet these three
goals and do so at minimum cost? - A lumber company uses labor (L) and capital (K) to produce joint
products, hardwood (H) and plywood (P). These items can be produced
by one of two processes:
Process 1: 1 unit of L and 2 units of K to yield 2 units of H and 1 unit of P
or
Process 2: 2 units of L and 2 units of K to yield 2 units of H and 4 units of P
Profit contribution is $2 per unit of H and $1 per unit of P. The firm has
110 units of L and 160 units of K available.
a. Formulate and solve the firm’s profit-maximization problem. (Hint:
Don’t be distracted by the fact that the processes produce joint
products. The correct decision variables are the levels of each process.)
b. Find the shadow price of labor.
c. Answer part (a), assuming the contribution of P rises to $3 per unit. - A 30-year-old investment analyst has been experimenting with Optimum
Eating, a new iPhone app. The app shows you how to divide the
proportion of your weekly meals among the four categories listed in the
following table. The table’s bottom two rows list the health attributes of
the meal categories. The row labeled BMI (standing for Body Mass
Index) rates the categories in terms of maintaining a trim and healthy
body weight. Healthy meals deliver a maximum BMI score (100); fast-
food meals deliver the worst score (20). The Heart row uses a similar
scale to rate the meals as to their impact on cardiovascular factors such
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