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# Problem 7-37 (Algorithmic)The New England Cheese Company produces two cheese spreads by

blending mild cheddar cheese with extra sharp cheddar cheese. The cheese spreads are packaged in 12-ounce containers, which are then sold to distributors throughout the Northeast. The Regular blend contains 65% mild cheddar and 35% extra sharp, and the Zesty blend contains 75% mild cheddar and 25% extra sharp. This year, a local dairy cooperative offered to provide up to 8100 pounds of mild cheddar cheese for \$1.30 per pound and up to 3500 pounds of extra sharp cheddar cheese for \$1.50 per pound. The cost to blend and package the cheese spreads, excluding the cost of the cheese, is \$0.30 per container. If each container of Regular is sold for \$1.80 and each container of Zesty is sold for \$2.10, how many containers of Regular and Zesty should New England Cheese produce? Do not round your interim computations. If required, round your answers to the nearest whole number.

Let R

number of containers of Regular

Z =

number of containers of Zesty

Optimal Solution: R = , Z = , profit = \$  .

Problem 6-23 (Algorithmic)

The medical community unanimously agrees on the health benefits of regular exercise, but are adults listening? During each of the past 15 years, a polling organization has surveyed americans about their exercise habits. In the most recent of these polls, slightly over half of all American adults reported that they exercise for 30 or more minutes at least three times per week. The following data show the percentages of adults who reported that they exercise for 30 or more minutes at least three times per week during each of the 15 years of this study.

Year

Percentage of Adults Who Exercise 30 or more minutes at least three times per week

1

41.8

2

44.5

3

47.6

4

44.7

5

46.6

6

48

7

48.2

8

51.3

9

49.6

10

49.2

11

49.7

12

53

13

51

14

54.8

15

52.9

a. Choose the correct time series plot.

(i)

(ii)

(iii)

(iv)

b.

Plot (iv)

Does a linear trend appear to be present?

Possible Positive Linear Trend

c.  use simple linear regression to find the parameters for the line that minimizes MSE for this time series. Do not round your interim computations and round your final answers to four decimal places. For subtractive or negative numbers use a minus sign. (Example: -300)

y-intercept, b0 =

Slope, b1 =

MSE =

d. Use the trend equation from part (b) to forecast the percentage of adults next year (year 16 of the study) who will report that they exercise for 30 or more minutes at least three times per week. Do not round your interim computations and round your final answers to four decimal places. For subtractive or negative numbers use a minus sign. (Example: -300)

%

e. Use the trend equation from part (b) to forecast the percentage of adults three years from now (year 18 of the study) who will report that they exercise for 30 or more minutes at least three times per week. Do not round your interim computations and round your final answers to four decimal places. For subtractive or negative numbers use a minus sign. (Example: -300)

%

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