At a peach packaging plant, 42,000 lbs of fresh peaches are processed and packed

Question

At a peach packaging plant, 42,000 lbs of fresh peaches are processed and packed each hour. The table shows the diminishing inventory of peaches over the hour. Remaining peaches are sent to another part of the facility for canning.

Peach Inventory

(a) Write the function for the linear model that gives peach inventory in thousand pounds, where t is measured in hours, with data from

0 t 1.00.

(Round all numerical values to three decimal places.)
P(t) = ______thousand pounds

(b) Use the model to estimate how many peaches are left in inventory after half an hour.


(c) Use the model to estimate how many peaches will be sent to canning.

Time, t
(hours) Peaches, P
(thousand pounds) 0 42 0.25 41 0.50 35 0.75 33 1.00 26

Explanation / Answer

a)

Following is the output for the regression model -

So, the required model is-

P(t) = 43.4 - 16(t)

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b)

According to the model, the predicted value for t=1 is-

P(t) = 43.4 - 16

P(t) = 27.4 thousands.

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c)

The remaining amount of peaches = 42 - 27.4 = 14.6

SUMMARY OUTPUT Regression Statistics Multiple R 0.972433277 R Square 0.945626478 Adjusted R Square 0.92750197 Standard Error 1.751190072 Observations 5 ANOVA df SS MS F Significance F Regression 1 160 160 52.17391304 0.005471515 Residual 3 9.2 3.066666667 Total 4 169.2 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 43.4 1.356465997 31.99490449 6.7097E-05 39.0831198 47.7168802 Time (t) -16 2.215099697 -7.223151185 0.005471515 -23.04943585 -8.950564154

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