Question

In: Math

A health club is trying to determine how to allocate funds for advertising. The manager decides...

A health club is trying to determine how to allocate funds for advertising. The manager decides to advertise on the radio and in the newspaper. Previous experience with such advertising leads the club to expect

A(r, n) = 0.1r2n responses

when r ads are run on the radio and n ads appear in the newspaper.
Each ad on the radio costs $8, and each newspaper ad costs $4. The manager is currently budgeting $336 for advertising. Therefore the constraint equation is given by

g(r, n) = 8r + 4n = 336 dollars

a) Write the Lagrange system that can be used to find the optimal point of

A(r, n)

subject to the given budget constraint. (Enter your answers as a comma separated list of equations. Use λ to represent the Lagrange multiplier.) You DO NOT need to solve the system.

The solution to the Lagrange system was found to be r=28, n=28, and λ=19.6.

(b) What is the optimal number of responses expected with the given advertising budget? (Round to the nearest whole number.)

(c) What are the units for λ?

(d) Suppose the manager budgeted an additional $26 for advertising. What is the approximate change in the optimal number of responses as a result of this change in the constraint level? (Round your answer to the nearest whole number.)

Solutions

Expert Solution

milcah answered 2 years ago
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