Final answer:
Amanda should allocate her $45,000 budget to reach 1,559,000 potential customers through a mix of website ads, social media ads, tradeshows, and print magazine ads, considering the relevant constraints. If the budget doubled, the additional funds could be used to increase social media ads and print frequency, possibly achieving a higher reach.
Step-by-step explanation:
To recommend an appropriate mix of advertising and promotions for Amanda's company, we must consider the cost and reach of each option as well as the constraints provided. Amanda has a minimum online presence requirement of 110 ads per year but cannot exceed one website ad per week. She also wants to attend at least three tradeshows and considers advertising in art magazines a maximum of once per month or as infrequent as once every three months. Given these conditions, we can calculate the optimal mix using Excel, considering the cost and reach of each option.
Scenario 1: Original $45,000 Budget
Art Website Ads (max 52 times a year): 52 ads × $250 = $13,000 for 728,000 reach.
Social Media Ads (to meet minimum online ads): (110 - 52) ads × $250 = $14,500 for 696,000 reach.
Tradeshows (at least 3 tradeshows): 3 tradeshows × $1,000 = $3,000 for 15,000 reach.
Print Magazine (once every three months for each magazine): 3 magazines × 4 times a year × $400 = $4,800 for 120,000 reach.
With this setup, we reach a total of 1,559,000 potential customers within the $45,000 budget. We meet the online presence minimum, attend the mandatory tradeshows, and have a recurring presence in print magazines.
Scenario 2: Doubled Budget to $90,000
If Amanda doubled her advertising budget to $90,000, the additional funds could be allocated to increase the number of social media ads and the frequency of magazine ads, while still respecting the maximum useful frequency of website ads and the value of attending tradeshows. This could significantly increase her reach.
For a precise answer, a similar calculation process would be repeated with the larger budget while considering the diminishing returns and saturation points for each advertising medium.