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Sagot :
The ticket price must be kept at $7.5 to maximise revenue generated from the selling of tickets.
What is a Function?
A function assigns the value of each element of one set to the other specific element of another set.
The cost of a ticket is represented by c, while the number of people who will attend the party is given by the formula (75-5c). Therefore, the total revenue that will be generated from the sale of the tickets is,
Revenue, (R) = c × (75 - 5c) = 75c - 5c²
Now, to know the maximum of the income, we must differentiate the function and then put it against 0. Therefore, the differentiation of the function will be,
[tex]\dfrac{dR}{dc} = 75-10c[/tex]
Now, if we substitute the value of the differentiated function with 0.
[tex]75-10c=0\\\\-10c =-75\\\\c = 7.5[/tex]
Hence, the ticket price must be kept at $7.5 to maximise revenue generated from the selling of tickets.
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