Lagrange multipliers for sports banquet revenue with group discounts

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bb155
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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.
 
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bb155 said:
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?