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Linear equations and constraints

The financial institution has asked your firm to place some spot advertisements. The financial institution wants you to find the best allocation of ads between 2 of the local media outlets.

The company you have chosen to handle the transaction has estimated the average number of potential new customers reached per spot announcement to be 1,500 for radio and 500 for newspaper. The price for each spot announcement is $500 for radio and $200 for newspaper as long as the minimum guaranteed number is exceeded. The customer wants a total of 45,000 potential customers reached for which they will pay $16,000. Find the proper number of spot announcements to fit the customer's request of potential customers reached and fee charged.

There are two standard plans for radio/newspaper ad combinations that give a reduced price (but same price for each spot) if you use them. These discounts are included in the $16,000 charge. The first spot plan is for the weekend and has one radio spot/weekend and one newspaper spot/weekend. The second spot plan is for during the 5-day work week and has two radio spots/week and four newspaper spots/week. These plans are also available on holidays but not at an extra discounted rate. Find the corresponding number of week and weekend spot plans.

Objective: Solve equations and systems of equations in two variables, formulate real-world problems in terms of linear equations and solve these systems by several commonly applied methods.

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The 4 pages solution shows in detail how to translates the date given in the question to equations and how to solve them.