Question

A factory sells backpacks for $40 each. The cost to make 1 backpack is $10.00. In addition to the costs of making backpacks, the factory has operating expenses of $12,000 per week. The factory’s goal is to make a profit of at least $980 each week. What is the inequality for the number of backpacks ,x, that need to be sold each week for the factory to meet this goal? How many backpacks must the factory sell to meet its weekly goal? Also give a statement.

Answer 1

980= (40-10)x - 12000= amount of PROFIT
12,980 = 30x; divide both sides by 30; and you get x=432.67
So the company would need to sell at least 433 backpacks to make a profit of at least 980 per week

Answer 2

Answer: x (40-10) -12000≥980

The factory must sell 433 backpacks to meet its weekly goal.

Explanation:

Hi, to answer this question we have to write an inequality.

So, since the backpacks (x) are sold by $40 and the cost of making one is $10, the revenue per bag is equal to 40x and the cost is 10x.

12,000 of operating expenses are also expenses.

So, for the profit:

Profit = revenue- cost

P = 40x-10x-12,000

P = x (40-10)-12000

The factory goal is to make a profit of at least $980 each week, so, the profit must be greater or equal than 980.

x (40-10) -12000≥980

Solving for x

30x-12000≥980

30x≥980+12000

30x ≥12980

x≥12980/30

x≥432.6

x≥433 (rounded, because if the sell 432 they will not meet the goal)

The factory must sell 433 backpacks to meet its weekly goal.