Question

A new business started and is selling calculus notes. for the first year, the fixed costs for setting up the new production line are $65. the variable costs for producing each set of notes are estimated at $4. the sales department decides that the notes can be sold during the first year at a price of $17 each.

a. find C(x), the total cost of producing x sets of notes.
b. find R(x), the total revenue from the sale of x sets of notes.
c. how many sets of notes must the business sell in order to break even?
a, b, and c aren't choices they are questions so please help me with them and maybe explain them as well

Answer 1

Answer: Hence, a) C(x)=65+4x

b) R(x)=17x

c) 5 sets of notes

Explanation:

Since we have given that

Fixed costs for setting up the new production line = $65

Cost for producing each set of notes = $4

Let the number of sets of notes be x

According to question ,

a) Total cost of producing is given by

`C(x)=65+4x`

b) Selling price of each notes = $17

According to question,

`R(x)=17x`

c) Break even point will be

`C(x)=R(x)\\\\65+4x=17x\\\\65=17x-4x\\\\65=13x\\\\x=(65)/(13)\\\\x=5`

At 5 sets of notes the business sell in order to break even.

Hence, a) C(x)=65+4x

b) R(x)=17x

c) 5 sets of notes