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Problem 10

# Let $$g(x, y, z)=0.01 x+0.02 y-0.03 z-0.05 .$$ Complete the following sentences. a. g ___ by ___ units for every 1 unit of increase in z. b. g ___ by ___ units for every 1 unit of increase in x. c. ______ by 0.02 units for every _______.

Expert verified
a. g decreases by 0.03 units for every 1 unit of increase in z. b. g increases by 0.01 units for every 1 unit of increase in x. c. g increases by 0.02 units for every 1 unit of increase in y.
See the step by step solution

## Step 1: Coefficients of x, y, and z in g(x, y, z)

The function g is given by $$g(x, y, z) = 0.01x + 0.02y - 0.03z - 0.05$$. The coefficients of x, y, and z are 0.01, 0.02, and -0.03, respectively.

## Step 2: a. Change in g with respect to z

The coefficient of z in the function is -0.03. So, g decreases by 0.03 units for every 1 unit of increase in z. The answer for sentence a: g decreases by 0.03 units for every 1 unit of increase in z.

## Step 3: b. Change in g with respect to x

The coefficient of x in the function is 0.01. So, g increases by 0.01 units for every 1 unit of increase in x. The answer for sentence b: g increases by 0.01 units for every 1 unit of increase in x.

## Step 4: c. Change in g with respect to y

The coefficient of y in the function is 0.02. So, g increases by 0.02 units for every 1 unit of increase in y. The answer for sentence c: g increases by 0.02 units for every 1 unit of increase in y.

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