You manage a buffet at a local restaurant. You charge $10 for the buffet. On average, 14 customers choose the buffet as their meal every hour. After surveying several customers, you have determined that for every $1 increase in the cost of the buffet, the average number of customers who select the buffet will decrease by 2 per hour. The restaurant owner wants the buffet to maintain a minimum revenue of $120 per hour. Part A Would the best representation of this scenario be an equation or an inequality? How do you know? Part B Write an expression representing the cost per customer. Assume that x represents the increase in the price of the buffet over $10.
You manage a buffet at a local restaurant. You charge $10 for the buffet. On average, 14 customers choose the buffet as their meal every hour. After surveying several customers, you have determined that for every $1 increase in the cost of the buffet, the average number of customers who select the buffet will decrease by 2 per hour. The restaurant owner wants the buffet to maintain a minimum revenue of $120 per hour.
Part A
Would the best representation of this scenario be an equation or an inequality? How do you know?
Part B
Write an expression representing the cost per customer. Assume that x represents the increase in the price of the buffet over $10.
Part C
Now write an expression representing the average number of customers. Assume that x represents the increase in the price of the buffet over $10.
Part D
To calculate the hourly revenue from the buffet, multiply the price paid by the customer and the average number of customers per hour. Use your expressions from parts B and C to create an equation or inequality that represents the desired revenue. Simplify, if possible.
Part E
Can you increase the buffet price by $3 and maintain the desired minimum revenue?
Part F
Can you increase the buffet price by $2 and maintain the desired minimum revenue?
Part G
Assuming that any increase occurs in whole dollar amounts, what is the maximum possible increase that maintains the desired minimum revenue? Explain why this is true.
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