Hi everyone!

The president of a small manufacturing firm is concerned about the continual increase in manufacturing costs over the past sever

mrs_skeptik [129]

Answer:

The answers to the question are

(a) The time series plot is given as attached

(b) The parameters for the line that minimizes MSE for the time series are;

y-intercept, b₀ = 19.993

Slope, b₁ = 1.77

MSE = 19.44

T $_t$ = 19.993 + 1.774·t

(c) The average cost increase that the firm is realizing per year is $ 1.77

(d) The estimate of the cost/unit for next year is $35.96.

Step-by-step explanation:

(a) Using the provided data, the time series plot is given as attached

(b) Given hat the y-intercept, = b₀

Slope = b₁

Therefore the linear trend forecast equation is given s

T $_t$ = b₀ + b₁·t

The linear trend line slope is given as

b₁ = $\frac{\Sigma^n_{t=1}(t-\overline{\rm t)}(Y_t-\overline{\rm Y)}}{\Sigma^n_{t=1}(t-\overline{\rm t} )^2}$

b₀ = $\overline{\rm Y}$ - b₁· $\overline{\rm t}$

Where:

Y $_t$ = Time series plot value at t

n = Time period number

$\overline{\rm Y}$ = Time series data average value and

$\overline{\rm t}$ = Average time, t

Therefore, $\overline{\rm t}$ = $\frac{\Sigma^n _{t=1} t}{n} = \frac{36}{8} =4.5$

$\overline{\rm t}$ = 4.5

$\overline{\rm Y}$ = $\frac{\Sigma^n _{t=1} Y_t}{n} = \frac{223.8}{8} =27.975$

$\overline{\rm Y}$ = 27.975

Therefore the linear trend line equation T $_t$ , is

b₁ = $\frac{\Sigma^n_{t=1}(t-\overline{\rm t)}(Y_t-\overline{\rm Y)}}{\Sigma^n_{t=1}(t-\overline{\rm t} )^2}$ = $= \frac{74.5}{42}$ = 1.774

b₀ = $\overline{\rm Y}$ - b₁· $\overline{\rm t}$ = 27.975 - 1.774×4.5 = 19.993

Therefore the trend equation for the linear trend is

T $_t$ = 19.993 + 1.774·t

MSE = $\frac{1}{2} \Sigma(Y-\overline{\rm Y)^ }^2$ = $\frac{155.495}{8}$ = 19.44

(c) From the linear trend equation, the average is given as the slope of the curve or b₁ which is equal to 1.774

Therefore the average cost increase that the firm has been realizing per year is $ 1.77

(b) From the equation of the future trend, we have when y = 9

T $_t$ is given as

T $_t$ = 19.993 + 1.774×9 = 35.96

The cost/unit for 9th year is $35.96

3 0

4 years ago

5 times the square root of x over 2 = 1

kati45 [8]

Here's a step-by-step in solving this equation:

$5 \sqrt{ \frac{x}{2} } = 1$
$\sqrt{ \frac{x}{2} } = \frac{1}{5} 
$
$\frac{ \sqrt{2x} }{2} = \frac{1}{5} 
$
$\sqrt{2x} = \frac{2}{5} 
$
$2x = \frac{4}{25}$
∴ $x = \frac{2}{25}$

3 0

4 years ago

Would I add the exponents with z to the fourth power?

Sloan [31]

When you have multiplying with same base, you add the power, for example here : z^6 * z^3 = z^(6+3) = z^9.

When you have dividing with the same base, you substract it, for example here : z^9/z^4 = z^(9-4) = z^5.

3 0

4 years ago

Please help!! Local wildlife experts have begun to track the population of trout in their area. The function f represents the ap

jeka57 [31]

Answer:

Option C.

Step-by-step explanation:

We know that

f(t) = 1.5t + 50

represents the approximate population of trout in Sky Lake

And

g(t) = 0.1t^2 - 4t + 70

represents the approximate population of trout in Lake Cyan

The total trout population in the area is described as

f(t) + g(t)

f(t) + g(t) = [1.5t + 50] + [0.1t^2 - 4t + 70]

f(t) + g(t) = [1.5t + 50+ 0.1t^2 - 4t + 70]

f(t) + g(t) = [0.1t^2 -2.5t + 120]

f(t) + g(t) = 0.1t^2 -2.5t + 120

Option C.

6 0

3 years ago

Given HIJ ≌ MNO and HI = 15, IJ = 8, and JH = 11, what is OM?

Irina-Kira [14]

I hope im not to late to help but the anwers is 11 because JH and OM the same :)

3 0

3 years ago