A profit function P ( x,y ) (in thousands of dollars) depends on the labor time

ID: 2846173 • Letter: A

Question

A profit function P(x,y) (in thousands of dollars) depends on the labor time per month x (in hundreds of hours) and manufacturing cost y (in hundreds of dollars). If no work is done, and nothing is spent on manufacturing, then there was no profit. It is known that 200 hours of labor and $500 on manufacturing resulted in a profit of $5000. However, with only 100 hours of labor and $600 on manufacturing led to a loss of $1000. Find a linear equation satisfying these requirements. A profit function P(x,y) (in thousands of dollars) depends on the labor time per month x (in hundreds of hours) and manufacturing cost y (in hundreds of dollars). If no work is done, and nothing is spent on manufacturing, then there was no profit. It is known that 200 hours of labor and $500 on manufacturing resulted in a profit of $5000. However, with only 100 hours of labor and $600 on manufacturing led to a loss of $1000. Find a linear equation satisfying these requirements. A profit function P(x,y) (in thousands of dollars) depends on the labor time per month x (in hundreds of hours) and manufacturing cost y (in hundreds of dollars). If no work is done, and nothing is spent on manufacturing, then there was no profit. It is known that 200 hours of labor and $500 on manufacturing resulted in a profit of $5000. However, with only 100 hours of labor and $600 on manufacturing led to a loss of $1000. Find a linear equation satisfying these requirements. A profit function P(x,y) (in thousands of dollars) depends on the labor time per month x (in hundreds of hours) and manufacturing cost y (in hundreds of dollars). If no work is done, and nothing is spent on manufacturing, then there was no profit. It is known that 200 hours of labor and $500 on manufacturing resulted in a profit of $5000. However, with only 100 hours of labor and $600 on manufacturing led to a loss of $1000. Find a linear equation satisfying these requirements.

Explanation / Answer

profit = a x time + b x cost

5000= 200a + 500b

-1000= 100a+600b

b= -10

a=50

profit = 50 x time - 10 x cost

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A profit function P ( x,y ) (in thousands of dollars) depends on the labor time

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