A health club is trying to determine how to allocate funds foradvertising. The manager decides to advertise on the radio and inthe newspaper. Previous experience with such advertising leads theclub to expect
A(r, n) =0.1r2n responses
when r ads are run on the radio and n adsappear in the newspaper.
Each ad on the radio costs $8, and each newspaper ad costs $4. Themanager is currently budgeting $336 for advertising. Therefore theconstraint equation is given by
g(r, n) =8r + 4n = 336 dollars
a) Write the Lagrange system that can be used to find theoptimal point of
A(r,n)
subject to the given budget constraint. (Enter your answers as acomma separated list of equations. Use λ to represent theLagrange multiplier.) You DO NOT need to solve the system.
The solution to the Lagrange system was found to ber=28, n=28, and λ=19.6.
(b) What is the optimal number of responses expected with thegiven advertising budget? (Round to the nearest whole number.)
(c) What are the units for λ?
(d) Suppose the manager budgeted an additional $26 foradvertising. What is the approximate change in the optimal numberof responses as a result of this change in the constraint level?(Round your answer to the nearest whole number.)
