Answer:
The answer to the questions asked is:
a) The maximum possible income for the museum is $4,840 per day.
b) The increase you must make to obtain the maximum income is $8 per ticket.
c) The income of the museum without increasing the fee is $4200.
Step-by-step explanation:
To solve all the questions asked, we must take into account the provided equation:
- <u>R = -10x2 + 160x + 4200
</u>
The first question asks for the maximum income, that is, the maximum amount of money that can be obtained by making increases in the rate, despite the loss of people, so you must replace the X in the equation with values until instead of increase decrease:
- R = -10 (1) 2 + 160 (1) + 4200 = 4350
- R = -10 (2) 2 + 160 (2) + 4200 = 4480
- R = -10 (3) 2 + 160 (3) + 4200 = 4590
- R = -10 (4) 2 + 160 (4) + 4200 = 4680
- R = -10 (5) 2 + 160 (5) + 4200 = 4750
- R = -10 (6) 2 + 160 (6) + 4200 = 4800
- R = -10 (7) 2 + 160 (7) + 4200 = 4830
- <u>R = -10 (8) 2 + 160 (8) + 4200 = 4840
</u>
- R = -10 (9) 2 + 160 (9) + 4200 = 4830
As you can see, when the increase is $9, the income falls, so <u>the maximum income is $4,840, while it can be seen that it occurs with an increase of $8, which answers the second question</u>.
For the third question, that is, the income of the museum without increasing the fee, you must remember that the variable X is the increase in the fee, therefore, if you want to obtain the income without an increase, it must be given a value of zero to the variable inside the equation, with which we obtain:
- <u>R = -10 (0) 2 + 160 (0) + 4200 = 4200</u>
