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 $3810.30 per day and variable costs of $0.91 per board-foot produced. Lumber sells for $2.21 per board-foot. A board-foot is a measure of volume.

At least how many board-feet must be sold for the lumber yard to make a profit?

Question

Mathematics

Clarissa Hamilton

22 June, 08:34

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 $3810.30 per day and variable costs of $0.91 per board-foot produced. Lumber sells for $2.21 per board-foot. A board-foot is a measure of volume.

At least how many board-feet must be sold for the lumber yard to make a profit?

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Answers (1)

Know the Answer?

Yair Young · Answer 1

Answer: at least, 2931 board feet

Step-by-step explanation:

Let x represent the number of board-feet of lumber yards that is produced and sold in a day

The lumber yard has fixed costs of $3810.30 per day and variable costs of $0.91 per board-foot produced. It means that the cost of producing x board-feet of lumber yards is

0.91x + 3810.3

Lumber sells for $2.21 per board-foot. It meas that the revenue from selling x board feet of lumber yard is 2.21x.

Profit = Revenue - total cost

In order to make profit, Revenue must be greater than total cost. Therefore,

2.21x ≥ 0.91x + 3810.3

2.21x - 0.91x ≥ 3810.3

1.3x ≥ 3810.3

x ≥ 3810.3/1.3

x ≥ 2931

The number of board-feet of lumber yard that must be sold to make profit is at least 2931