Solve

using Ampl code

1-1. This exercise starts with a two-variable linear program similar in structure to the one of Sec- tions 1.1 and 1.2, but with a quite different story behind it. (a) You are in charge of an advertising campaign for a new product, with a budget of $1 million. You can advertise on TV or in magazines. One minute of TV time costs $20,000 and reaches 1.8 million potential customers; a magazine page costs $10,000 and reaches 1 million. You must sign up for at least 10 minutes of TV time. How should you spend your budget to maximize your audi- ence? Formulate the problem in AMPL and solve it. Check the solution by hand using at least one of the approaches described in Section 1.1. (b) It takes creative talent to create effective advertising; in your organization, it takes three person-weeks to create a magazine page, and one person-week to create a TV minute. You have only 100 person-weeks available. Add this constraint to the model and determine how you should now spend your budget. (c) Radio advertising reaches a quarter million people per minute, costs $2,000 per minute, and requires only 1 person-day of time. How does this medium affect your solutions? (d) How does the solution change if you have to sign up for at least two magazine pages? A maxi- mum of 120 minutes of radio