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Soloha48 [4]
3 years ago
11

The amphitheater has two types of tickets available, reserved seats and lawn seats. The maximum capacity of the venue is 20,000

people. However, they must sell at least 5,000 tickets to hold a concert. As an additional constraint, the number of lawn seats cannot exceed the number of reserved seats. If reserved seats profit $65 each and lawn seats profit $40 each, how many of each seat must they sell to maximize profit?

Mathematics
1 answer:
Tema [17]3 years ago
8 0

Let the number of reserved tickets = x

Let the number of lawn seats = y

Constraint functions:

Maximum capacity means x+y\leq 20000

For concert to be held x+y\geq 5000

lawn seats\leq reserved means y\leq x

Objective functions :

Maximum profit equation p = 65x +40y

Intersection points :

(10000,10000) (20000,0)(2500,2500)(5000,0)

p at (10000,10000) = 65(10000) + 40(10000) = $1050000

p at (20000,0) = 65(20000) + 40(0) = $1300000

p at (2500,2500) = 65(2500) + 40(2500) = $262500

p at (5000,0) = 65(5000) + 40(0) =  $325000

Hence maximum profit occurs when all 20000 reserved seats are sold and the profit is $1300000

Please find attached the graph of it.

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Troyanec [42]

Answer:

<em>x </em>equals 3.6.

Step-by-step explanation:

A way to solve this equation is to preform the inverse operations on both sides.

1. Add 19 to -19 and 5: 5<em>x </em>+ 6 - 19 + 19 = 5 + 19  ---> 5x + 6 = 24

2. Subtract 6 from 6 and 5: 5x + 6 - 6 = 24 - 6 ---> 5x = 18

3. Divide 5x and 18 by 5: 5x / 5 = 18 / 5 ---> x = 3.6

4. 3.6 is the answer.

To prove it, substitute x with 3.6 in the equation: 5 · 3.6 + 6 - 19 = 5

I hope this made sense and helped you a lot! :)

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3 years ago
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igor_vitrenko [27]

Answer:

5

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5 0
3 years ago
Assign a variable to each quantity and write each statement as an inequality. Then give an example
RideAnS [48]

Answer:

1.

Variable: x

Inequality: x ≤ 12

Value that matches: 12

2.

Variable: y

Inequality: y < 66

Value that matches: 60

Step-by-step explanation:

Solving (1):

Let x be the variable

Reading through the question, we have the inequality to be represented by "at most".

At most is used for less than or equal to.

Hence, the expression can be represented by:

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The range of this inequality is limited to all natural number that do not exceed 12.

Examples are 8, 2, 11, 12

Solving (2):

Let the variable be y

Reading through the question, we have the inequality to be represented by "below".

Below means less than

Hence, the expression can be represented by:

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The range of this inequality is limited to all number less than 66.

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6 0
3 years ago
at a golf course, a worker placed 216 golf balls equally into 9 buckets. what is the ratio of golf balls to buckets?
ankoles [38]
The ratio is 216:9, which can be simplified to 72:3, which can be simplified to 34:1. This can also be written as a fraction (34/1). It means there are 34 golf balls for every one bucket.
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3 years ago
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-3(-4n + 30) = -30 need help​
DIA [1.3K]

First we will do -3 times everything in the parenthesis.

-3 times -4n = 12n

-3 times 30 = -90

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12n - 90 = -30

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12n = 60

divide 12 on both sides;

n = 5

This is your answer,

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