Question

Benjamin's Backpacks can sell backpacks for ​$30 per backpack. The costs for making the backpacks are a fixed cost of ​$400 and a production cost of ​$10 per backpack. ​a) Write the cost and revenue equations. ​b) Graph both​ equations, for 0 to 50​ backpacks, on the same axes. ​c) Use the graph to estimate the number of backpacks​ Benjamin's Backpacks must sell to break even. ​d) Write the profit formula. ​e) Use the profit formula to determine whether​ Benjamin's Backpacks makes a profit or loss if it sells 40 backpacks. What is the profit or​ loss? ​f) How many backpacks must​ Benjamin's Backpacks sell to realize a profit of​ $1000?

Answer 1

Let be the number of bagpacks and be the revenue and cost of bagpacks respectively.

Then,

(a)

Is the cost equation.

is the revenue equation.

(b)

The graph is attached below.

Horizontal axis if for x.

(c)

Break even point is the point of intersection (20,600).

So, the number of bagpacks = 20

(d)

Profit = Revenue - cost

Hence,

is the profit function.

(e)

For ,

Sign is positive so he makes a profit of $ 400.

(f)

To make profit $ 1000.

Hence, he needs to sell 70 bagpacks.