# Finding the Optimal Number of Advertising Hours

Problem: "Optimal Input Level."

Ticket Services, Inc., promotes concerts and sporting events. The college uses a team of ten students to hand deliver flyers at the mall, where every hour increment of flyer advertising costs $130. Over the past year, the following relation between advertising and ticket sales per event has been observed:

Sales (units) = 7,000 + 200A - 0.6A2 and ∆Sales/∆A = 200 - 1.2A

Here A represents one hour of flyer distribution and sales are measured in numbers of tickets.

Joe Smith, a senior student and team-leader has been asked to suggest an appropriate level of advertising. In thinking about this problem, Joe noted its resemblance to the optimal resource employment problem he had studied in a Managerial Economics course. The advertising-sales relation could be thought of as a production function with advertising as an input and sales as the output. The problem is to find the level of advertising that maximizes sales. After consultation with faculty in the Business Department, he determines that the value of output is $2 per ticket, the net marginal revenue earned (price minus all marginal costs except flyer advertising).

A. Continuing with Smith's production analogy, what is the marginal product of advertising?

B. Using the rule for optimal resource employment, determines the profit-maximizing number of flyer distribution hours.

https://brainmass.com/economics/production-function/finding-the-optimal-number-of-advertising-hours-573338

#### Solution Preview

A. Continuing with Smith's production analogy, what is the marginal product of advertising?

Marginal product of ...

#### Solution Summary

This solution depicts the required steps needed to find the optimal number of advertising hours in the given case.

Linear Programming - Graphical and Computer Methods - Answer: Problem 6-36, Problem 7-16 & Problem 7-29

6-36 Ralph Janaro simply does not have time to analyze all

of the items in his company's inventory. As a young

manager, he has more important things to do. The

following is a table of six items in inventory along

with the unit cost and the demand in units.

iDENTIFlcxnoN CODE' . UNIT COST ($) DEMAND IN UNITS

XXI 5.84 1,200

B66 5.40 1,110

3CPO 1.12 896

33CP 74.54 1,104

R2D2 2.00 1,110

RMS 2.08 961

(a) Find the total amount spent on each item during

the year. What is the total investment for all of

these?

(b) Find the percentage of the total investment in

inventory that is spent on each item.

(c) Based on the percentages in part (b), which

item(s) would be classified in categories A, B, and

C using ABC analysis?

(d) Which item(s) should Ralph most carefully control

using quantitative techniques?

7-16 A candidate for mayor in a small to 'In has allocated

" $40,000 for last-minute advertising in the days preceding

the election. Two types of ads will be used:

radio and television. Each radio ad costs $200 and

reaches an estimated 3,000 people. Each television ad

costs $500 and reaches an estimated 7,000 people. In

planning the advertising campaign, the campaign

manager would like to reach as many people as pOSSible,

but she has stipulated that at least 10 ads of each

type must be used. Also, the number of radio ads

must be at least as great as the number of television

ads. How many ads of each type showd be used? How

many people will this reach?

7-29 Graphically analyze the following problem:

maximize profit = $4X + $6Y

Subject to: X + 2Y O;8 hours

6X + 4Y O; 24 hours

(a) What is the optimal solution?

(b) If the first constraint is altered to X + 3 Y:O; 8, does

the feasible region or optimal solution change?