Optimizing Revenue for a Sports Banquet

[bb155]

A hall charges $30 per person for a sports banquet. For every group of over 50, the hall will decrease the price by $10 per person, in excess of 50 people.

a. Write revenue as a multivariable function of the number of people, q, in excess of 50 and the price per person, p.

b.Write a constraint equation for the price in terms of the number of people in excess of 50

c.Maximize the revenue under the contstraint using the method of Lagrange Multipliers.

I just can't figure out b and c.. can anyone lend some help? As far as #A I have found that Revenue = 1700-10q and that when q=85 revenue is maximized.

 

[Mark44]

A hall charges $30 per person for a sports banquet. For every group of over 50, the hall will decrease the price by $10 per person, in excess of 50 people.

a. Write revenue as a multivariable function of the number of people, q, in excess of 50 and the price per person, p.

b.Write a constraint equation for the price in terms of the number of people in excess of 50

c.Maximize the revenue under the contstraint using the method of Lagrange Multipliers.

I just can't figure out b and c.. can anyone lend some help? As far as #A I have found that Revenue = 1700-10q and that when q=85 revenue is maximized.

Part a asks for the revenue as a function of q and p, R(q, p). What did you get as that function?