Promotional Budgeting.

The Westchester Chamber of Commerce periodically sponsors public service seminars and

programs. Currently, promotional plans are under way for this year$$s program. Advertising

alternatives include television, radio, and online. Audience estimates, costs, and maximum media

usage limitations are as shown.

Constraint Television Radio Online

Audience per advertisement $100,00018,00040,000$

Cost per advertisement $$2000$ $$300$ $$600$

Maximum media usage $102010$

To ensure a balanced use of advertising media, radio advertisements must not exceed $50\%$ of

the total number of advertisements authorized. In addition, television should account for at least

$10\%$ of the total number of adveThe Pfeiffer Company manages approximately $$15$ million for clients. For each client, Pfeiffer

chooses a mix of three investment vehicles: a growth stock fund, an income fund, and a money

market fund. Each client has different investment objectives and different tolerances for risk. To

accommodate these differences, Pfeiffer places limits on the percentage of each portfolio that

may be invested in the three funds and assigns a portfolio risk index to each client.

Here$$s how the system works for Dennis Hartmann, one of Pfeiffer$$s clients. Based on an

evaluation of Hartmann$$s risk tolerance, Pfeiffer has assigned Hartmann$$s portfolio a risk index

of $0\mathrm{.}05($maximum$).$ Furthermore, to maintain diversity, the fraction of Hartmann$$s portfolio

invested in the growth and income funds must be at least $10\%$ for each, and at least $20\%$ must

be in the money market fund.

The risk ratings for the growth, income, and money market funds are $0\mathrm{.}10,0\mathrm{.}05,$ and $0\mathrm{.}01,$

respectively. A portfolio risk index is computed as a weighted average of the risk ratings for the

three funds where the weights are the fraction of the portfolio invested in each of the funds.

Hartmann has given Pfeiffer $$300,000$ to manage. Pfeiffer is currently for

$$18,200.$

a$.$ How ma