Every year, Heather hosts a holiday party for her friends. Her party budget is $200. Heater spends her budget on food platters that cost $25 each and on entertainment, which costs $50 per hour.

a. Graph Heather's budget constraint for food and entertainment.
b. To reward her loyal business, the entertainment company Heather hires has offered her a 50 percent discount on entertainment purchases for this year's party. On your graph, illustrate Heather's new budget constraint for food and entertainment.
c. Assuming that food platters and entertainment are normal goods, what can you say about the quantity of each good that Heather will purchase after the discount? Will the quantity of entertainment increase or decrease, or is the change uncertain? Will the quantity of food increase or decrease, or is the change uncertain?

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Consider the scenario below and let us know if you believe lauren smith's actions to be ethical. let us know why or why not. lauren smith is the controller for sports central, a chain of sporting goods stores. she has been asked to recommend a site for a new store. lauren has an uncle who owns a shopping plaza in the area of town where the new store is to be located, so she decides to contact her uncle about leasing space in his plaza. lauren also contacted several other shopping plazas and malls, but her uncle’s store turned out to be the most economical place to lease. therefore, lauren recommended locating the new store in her uncle’s shopping plaza. in making her recommendation to management, she did not disclose that her uncle owns the shopping plaza. if management decided to go with lauren's uncle's plaza, what additional information would be needed in the financial statements?

Describe three scenarios in which you might utilize mathematics to investigate a crime scene, accident scene, or to make decisions involving police practice. be sure to explain how math is used in police as they work through each scenario.