Answer:
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Noah manages a buffet at a local restaurant. He charges $10 for the buffet. On average, 16 customers choose the buffet as their meal every hour. After surveying several customers, Noah has 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 $130 per hour.
Noah wants to model this situation with an inequality and use the model to help him make the best pricing decisions.
To calculate the hourly revenue from the buffet after x $1 increases, multiply the price paid by each customer and the average number of customers per hour. Create an inequality in standard form that represents the restaurant owner’s desired revenue.
Type the correct answer in each box. Use numerals instead of words.
x2 + x + ≥
Price is $8
Step-by-step explanation:
The minimum revenue of $130 is a function price multiplied by number of buffet sold
initially price per buffet was $10
16 buffet sold per hour
when cost of buffet to customer increases by $x,the number of customer would decrease by 2 multiplied x since x is the increase in the price that has turned customers away
(10+x)(16-2x) less than or equals 130
by opening brackets we have
160+16x-20x-2x^2 less than equals 130
if we divide the equation by 2
80+8x-10x-x^2
8(10+x)-x(10+x)
8-x=0 or x+10=0
x=8 0r -10
price cannot be negative hence x is $8
