Question

Assume that the cost to produce an item is a linear function and all items produced are sold. A lumber yard has fixed costs of $2230.80 per day and variable costs of $0.03 per board-foot produced (a board-foot is a measure of volume). The lumber then is sold for
$1.13 per board-foot. How many board-feet must be sold for the lumber yard to make a profit? Write the inequality, solve and interpret the results.

show work please

Answer 1

Answer:

1.13x > 2230.80 + 0.03x

x > 2028

(more than 2028 or atleast 2029)

Step-by-step explanation:

Revenue = 1.13x

Cost = 2230.8 + 0.03x

Profit: Revenue > Cost

1.13x > 2230.8 + 0.03x

1.13x - 0.03x > 2230.80

1.1x > 2230.8

x > 2028

More than 2028 board feet must be produced in order to make profit.

At 2028, there's no profit no loss

Answer 2

Answer:

see below

Step-by-step explanation:

The costs are

2230.80 + .03 b  where b is the board foot

the income was 1.13b

Profit is income - costs

Profit = 1.13b - (2230.80 + .03 b)

Distribute

         = 1.13b - .03b - 2230.08

         = 1.10b - 2230.08

Profit is when  the money is greater than 0

(breaking even is 0)

0 <1.10b - 2230.08

Add 2230.08 to each side

2230.08 < 1.10b - 2230.08 + 2230.08

2230.08 < 1.10b

Divide by 1.10

2230.08/1.10 < 1.10b/1.10

2027.345455 <b

They must sell at least 2027.345 board feet of lumber per day to make a profit