Grade 11 Math

Question

Last year, a banquet hall charged $30 per person, and 60 people attended the hockey banquet dinner. This year, the hall's manager has said that for every 10 extra people that attend the banquet, they will decrease the price by $1.50 per person. What size group would maximize the profit for the hall this year?

Answer 1

x represents each increase/decrease

c = (30 - 1.5x)(60 + 10x)

c = 1800 + 300x - 30x - 15x²

c = -15x² + 270x + 1800

 

Maximum occurs at -b/2a,or -270/(2)(-15), or 9

 

What size group produces the best deal?