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.

Question

Mathematics

Lane Glenn

21 April, 15:57

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.

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Answers (1)

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Alaina Moran · Answer 1

2028 ft

Step-by-step explanation:

Let the feets of boards sold to get profit be x hence with the price of $1.13 which is inclusive of profit, the total sales will be 1.13 x

The cost per day will equally be the sum of variable cost which considers the feets of boards and the daily fixed charge. Considering the variable of $0.03 and fixed charge of $2230.80 then the equation is represented as 0.03x+2230.80

Relating the two equations then

1.13x=0.03x+2230.80 and rearranging like terms

1.13x-0.03x=2230.80

1.1x=2230.8

X=2230.8/1.1=2,028 ft

Therefore, to maximize daily profit, 2028 ft must be sold