1. A brand manager for ColPal Products must determine how much time to allocate between radio and television advertising during the next month. Market research has provided estimates of the audience exposure for each minute of advertising in each medium, which it would like to maximize. Costs per minute of advertising are also known, and the manager has a limited budget of $25,000. The manager has decided that because television ads have been found to be much more effective than radio ads, at least 70% of the time should be allocated to television.

Suppose that we have the following data:

Type of Ad Exposure/Minute Cost/Minute

Radio 350 $400

TV 800 $2,000

a.Identify the decision variables, objective function, and constraints in simple verbal expressions.

b.Mathematically formulate a linear optimization model.

2. Implement the linear optimization model that you developed for ColPal Products in Problem 2 in Excel and use Solver to find an optimal solution.

3.Ensurethat thenumberofminutesofeach typeofadareinteger valued. How much difference is there between the optimalintegersolution and the linear optimization solution? Would rounding the continuous solution have provided the optimal integer solution?