Question

5) February is a busy time at Charlie's Chocolate Shoppe! During the week before Valentine's Day, Charlie advertises that his chocolates will be selling for $1.80 a piece (instead of the usual $2.00 each). The fixed costs to run the Chocolate Shoppe total $450 for the week, and he estimates that each chocolate costs about $0.60 to produce. Charlie estimates that he can produce up to 3,000 chocolates in one week. a) Write a function, C(n), to represent Charlie's total costs for the week if he makes n chocolates b) Write a function. R(n), to represent the revenue from the sale of n chocolates during the week before Valentine's Day. c) Write a function. P(n), that represents Charlie's profit from selling n chocolates during the week before Valentine's Day. Show complete work to find the function.​

Answer 1

a)
`C(n) = 450+0.60n` where
`n<=3000`

b)
`R(n) = 1.80n` where
`n<=3000`

c)
`P(n) = - 450 +1.20n`

Explanation:

Sale price of chocolates = $1.80 per chocolate

Fixed cost for the Chocolate Shoppe per week = $450

Cost to produce one chocolate = $0.60

Cost to produce
`n` chocolates = $0.60
`* n`

a) Cost function to represent the total cost for the production of
`n` chocolates :

`C(n) = 450+0.60n` where
`n<=3000`

b) Revenue function to represent the revenue from the sale of
`n` chocolates:

`R(n) = 1.80n` where
`n<=3000`

c) Profit function to represent Charlie's profit from selling
`n` chocolates:

Profit is nothing but revenue minus sales.

`P(n) = R(n) - C(n) \\P(n) = 1.80n - 450 -0.60n\\P(n) = - 450 +1.20n`