A) Demand function
price (x)          demand (D(x))
4                      540
3.50                  810
D - 540          810 - 540
----------- =  -----------------
x - 4               3.50 - 4
D - 540 
----------- = - 540
x - 4
D - 540 = - 540(x - 4)
D = -540x + 2160 + 540
D = 2700 - 540x
D(x) = 2700 - 540x
Revenue function, R(x)
R(x) = price * demand = x * D(x)
R(x) = x* (2700 - 540x) = 2700x - 540x^2
b) Profit, P(x)
profit = revenue - cost
P(x) = R(x) - 30
P(x) = [2700x - 540x^2] - 30
P(x) = 2700x - 540x^2 - 30
Largest possible profit => vertex of the parabola
vertex of 2700x - 540x^2 - 30
When you calculate the vertex you find x = 5 /2
=> P(x) = 3345
Answer: you should charge a log-on fee of $2.5 to have the largest profit, which is $3345.
        
             
        
        
        
Answer:
The corrext answer is, 512.
 
        
                    
             
        
        
        
X^2 + 4x - 16 - 11/(x + 2)
        
             
        
        
        
Answer:
3/8ths of 680 kcal or 3 x 85 = 255 kcal.
Step-by-step explanation:
3/8ths of 680 kcal or 3 x 85 = 255 kcal.
 
        
                    
             
        
        
        
Answer: $216
Step-by-step explanation:
Hope it helped