Answer to Question #312887 in Algebra for Shelly

Question

BAT Industries is a manufacturer of orange juice in Jamaica. In 2022 it sold a bottle of orange juice to wholesalers for $100 and its variable costs is $40 and fixed costs is $100,000 monthly:

 

 

Using the information provided. 

 

i. How many bottles of orange juice must the company sell in order to break even and what is the breakeven revenue? 

 

 

 

ii. If the company sold 1,500,000 bottles of orange juice for the year 2022, what was its profit? 

 

 

 

iii. Due to inflation, in 2023 fixed costs are expected to rise to $175,000 monthly. What will be the NEW break-even quantity and revenue? 

 

 

 

iiii. If the company will sell the same number of orange juice as it did in 2022 and it wants to make the same profit as in 20222, what price should they sell each bottle of orange Juice for in 2023? 

 

 Can some working out be shown please?

Answer 1

Let company sold n bottles. The cost of production of n bottles is $40*n + $100,000. After the sale of all bottles, the company will receive $100*n. The breakeven occurs when these two quantities are equal. So

40*n+100,000 = 100*n or 60*n = 100,000. Therefore breakeven quantity n = 1,667, and revenue is $166,700

ii

The profit the different between еру amount received per sale of n bottles and there production cost:

$100*n - ($40*n + $100,000) = 60*n - 100,000. So if n = 1,500,000 the profit is $89,900,000

iii

New breakeven quantity defined by 40*n + 175,000 = 100*n, so n = 2,917 and revenue is $291,700

iiii

The profit for 2022 is 60*n-100,000, the profit for 2023 year will be (p-40)*n-175,000, where p is the new price. If they are equal 60*n - 100,000 = (p-40)*n - 175,000, so (p-100)*n = 75,000 and

p = 100 + 75,000/n. Substitute n=1,500,000 get p = 100.05. So new price should be $100.05