A concert promoter finds she can sell 1000 tickets at $50 each. She will not sell the tickets for less than $50, but she finds that for every $1 increase in the ticket price above $50, she will sell 10 fewer tickets.(a) Express n, the number of tickets sold, as a function of p, the price.(b) Express R, the revenue, as a function of p, the price.(c) Find the domain of the function found in part (b).(d) Express R, the revenue, as a function of n, the number sold.(e) Find the domain of the function found in part (d).(f) Find the price that produces the maximum revenue.(g) Find the number of tickets sold that produces the maxi- mum revenue.(h) Find the maximum revenue.(i) Sketch the graph of the function found in part (b).(j) Describe what the graph found in part (i) tells you about how the revenue varies with price.
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
A concert promoter finds she can sell 1000 tickets at $50 each. She will not sell the tickets for less than $50, but she finds that for every $1 increase in the ticket price above $50, she will sell 10 fewer tickets.
(a) Express n, the number of tickets sold, as a function of p, the price.
(b) Express R, the revenue, as a function of p, the price.
(c) Find the domain of the function found in part (b).
(d) Express R, the revenue, as a function of n, the number sold.
(e) Find the domain of the function found in part (d).
(f) Find the price that produces the maximum revenue.
(g) Find the number of tickets sold that produces the maxi- mum revenue.
(h) Find the maximum revenue.
(i) Sketch the graph of the function found in part (b).
(j) Describe what the graph found in part (i) tells you about how the revenue varies with price.
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