The Cost of producing n items is given as C = 5 + 2n, where 5 is initial cost and 2 is a cost per item. Profit is given as P = 3n – 2 where 2 are initial expenses and 3 is a price for unit. Find the number of units we need to sell to make profit cover the costs (break-even point). Please show the entire solution

7 units

Step-by-step explanation:

If we want the profit to break even with the cost, then we must make the equations for cost and profit equal to each other.

3n-2=5+2n

First, we can subtract 2n from both sides and we get :

n-2=5

Next, we add 2 to both sides, and we get :

n=7

Therefore, we will need 7 units to break even with the cost and profit.

step-by-step explanation:

y = | -2(-2) |     →     y = | 4 |     →     y = 4       ⇒   (-2, 4)

y = | -2(-1) |     →     y = | 2 |     →       y =   2       ⇒   (-1, 2)    

y = | -2(0) |     →     y = | 0 |     →       y = 0         ⇒   (0, 0)

y = | -2(1) |   c →     y = | -2 |     →     y =   2         ⇒   (1, 2)    

y = | -2(2) |     →     y = | - 4 |     →     y =   4         ⇒   (2, 4)