We can write that as a function:
where is the number of price reductions. We can see that it is a quadratic function which has the biggest value at P = (p, q). It means that p is the number of reductions which results in the biggest profit.
It means that it's the best to make 2 price reductions for the company. The tickets should be sold for $200 - 2 * $20 = $160. It results in 2 * 50 more tickets sold which is 300 + 100 = 400.
Answer:
Ticket price: $160
Number of tickets: 400
Step-by-step explanation:
The amount spent on the ingredients = $20.16
The number of servings prepared = 15
The profit to b made in total = $20.00
Let us assume the minimum selling amount of per serve of lemonade = $ m
So, the selling amount of 15 per serving = 15 x ( cost of each serving)
= 15 x ( $ m) = 15 m
Now, Profit = Total Selling price - Total Cost price
⇒ $20 = 15 m - $20.16
or, 40.16 = 15 m
or, m =
⇒ m = 2.6773333
Now, rounding off to nearest hundredth, as 7 > 5 so 2,677333 ≈ 2.68
Hence, they should charge $2.68 per lemonade serving in order to earn $20 profit in total.