Question

2) Two teachers decide to start a line of customizable mechanical pencils so that pencils can be returned to students if they lose them. It costs them $5 to produce one pencil, and they have fixed costs of $300 for factory space and $500 for advertising at Staples. The teachers will either sell the pencils for $8 or for $50. Write an equation for the company’s costs:Determine which price option you would choose and why.How much of the product must be sold to break even (using your chosen selling price)?What are some things the company could do to increase their profit?

Answer 1

First lets figure out the costs

500+300 +5x where x is the number of pencils

800 +5x

Costs

C(x) = 800+5x

I would chooses 8 for the price of a pencil. No student would pay 50 dollars for a pencil

To break even

8x = 800+5x

Subtract 5x from each side

8x - 5x = 800+5x-5x

3x = 800

Divide each side by 3

3x/3 = 800/3

x = 266.67

We would need to sell at least 267 pencils to break even

To increase their profit, they could increase the selling price of the pencils. They could do more advertising of their pencils to sell more pencils.