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4 years ago

9

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

2 answers:

____ [38]4 years ago

5 0

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

UkoKoshka [18]4 years ago

4 0

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

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$\frac {dA}{dx}=0$

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Check this point by double differentiation

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Put this value back to equation (iii) to get the maximum value of area function. We have

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$\Rightarrow A=253.125 m^2$

Hence, the range of area function is $(0, 253.125 m^2]$ .

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