Question

Management is planning to promote a new service in two media buys: flyers and online advertisements. A media budget of $1,500 is available for this promotional campaign. Based on past experience in promoting its other services, the following estimate of the relationship between sales and the amount spent on promotion in these two media is

                              S = -8F^2 - 22A^2 - 4FA + 12F + 32A

where

                             S = total sales in thousands of dollars

                             F = dollars spent on flyers

                             A = dollars spent on online advertising

Formulate an optimization problem that can be solved to maximize sales subject to the media budget of spending no more than $1,500 on total advertising. Determine the optimal amount to spend on flyers and online advertising.

How much should be allocated to flyers and online advertising?
(in 000s, two decimal places - include leading zero, no dollar sign).

a. Flyers:

b. Online Ads:

What is the optimal sales value generated?
(in 000s, two decimal places, no dollar sign).

c. Sales:

How much of the budget is unspent, based on your optimization?
(in 000s, two decimal places - include leading zero, no dollar sign).

d. Unspent budget:

Answer 1

Let the sales be written as a function of two variables and

To find the critical points, we find the first-order partial derivative of the above equation w.r.t. and
and equate it to zero

The above two equations have two variables hence it can be solved,

and

The amount spent on online advertising in 000s would be

The amount spent on online advertising in 000s would be

The optimum sales value can be generated by plugging the values of and in the function of

Converting the sales value in 000s will give

Total budget spent on advertising =

Therefore, the unspent budget would be =>