Question

HELP PLS (This is Linear programming)- 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 for a concert to be held. As a additional constraint the number of lawn seats can't exceed the number of reserved seats. If reserved seats profit 65$ each and lawn tickets profit 40$ each, how many of each must they sell to maximize their profits.

- Will give brainliest answer

Answer 1

I have to look at my notes again but I know your two equations are gonna be...


S= reserved seats L = lawn chairs

S + L = 5000

40L + 65S = 20,000$

now you just solve the bottom one for each variable for itself then plug that in your top for the amount in each and how many of which ticket was sold.

Answer 2

Answer:

Let the number of reserved tickets be x

Let the number of lawn seats be y

Constraint functions are:

Maximum capacity means $x+y\leq 20000$

Condition for concert to be held is: $x+y\geq 5000$

We also have : lawn seats<reserved seats

means $y\leq x$

Maximum profit equation is:

$p=65x+40y$

If we graph the functions, we will get the following 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 $1,300,000.

Please find the graph attached.