A movie theater has fixed costs of 3000 per day and variable...

A movie theater has fixed costs of $3000 per day and variable costs averaging $7 per customer. The theater takes in an average revenue of $11 per customer. Find the cost function $C$, and revenue function, $R$, for $q$ customers. Select the correct graphs for $C$ and $R$, and find the break-even point. $C = $ $R = $ The graphs of $C$ and $R$ are: NOTE: Drag the point to select the graphs. p($) Figure 2 C R The break-even point is at $q = $ tickets.

Transcript

00:01 Okay, so we have a movie theatre with a fixed cost of $5 ,000 per day, and variable cost averaging $2 per customer, and the theatre charges $7 per customer.

00:13 We want to know how many customers per day does the theatre need in order to make a profit, and we want to find the cost and revenue functions and graph them on the same axes.

00:23 So i'm going to find the cost and revenue functions first, because this just makes part a easier.

00:28 So if we have that n is the number of customers, well, per day, the cost is going to be a function of n, and it's going to be 5 ,000.

00:45 So every day we have to pay 5 ,000 in costs, plus $2 per customer.

00:52 So 5 ,000 plus 2 times the number of customers.

00:55 This is going to be the cost function, c of n, and the revenue function, sorry, revenue as a function of n, or every customer that comes in pay $7, so it's just going to be seven times the number of customers n.

01:11 So this is the cost function, this is the revenue function, and we can use this for part a.

01:17 How many customers per day does the theatre need in order to make a profit? well, we can write the profit function if we want.

01:24 This is just going to be the revenue function, r of n, minus the costs.

01:30 So the revenue minus the costs, which is 5 ,000, no, not 5 ,000, sorry, this is mistake.

01:42 7n minus 5 ,000 minus 2n, which is 5n minus 5 ,000.

01:53 And we want there to be a profit.

01:56 So we want this function to be greater than 0.

01:58 So if this function is less than zero, this means we're making losses...

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