In: Statistics and Probability
This needs to be done in Excel and that is where I am having issues
Healthy Snacks Co. produces snack mixes. Recently, the company has decided to introduce a new snack mix that has peanuts, raisins, pretzels, dries cranberries, sunflower seeds and pistachios. Each bag of the new snack is designed in order to hold 250 grams of the snack. The company has decided to market the new product with a emphasis on its health benefits. After consulting nutritionists, Healthy Snacks decides to mix the ingredients so that the snack has the following specifications:
1 - Total calories <= 800
2 - Fat <= 20
3 - Sodium <= 200
4 - Potassium <= 700
5 - Carb <= 140
6 - Protein >= 10
7 - Vitamin A >= 3
8 - Vitamin B6 >= 25
9 - Vitamin C >= 2
10 - Iron >= 15
11 - Calcium >= 5
Table below shows the amount of each nutrition in each snack's ingredient per 1 gram:
peanut |
raisin |
pretzel |
dried cranberries |
sunflower seed |
pistachio |
|
Calories |
5.67 |
3.00 |
1.00 |
3.08 |
5.84 |
5.62 |
Fat (g) |
0.49 |
0.00 |
0.01 |
0.01 |
0.51 |
0.06 |
Sodium (mg) |
0.18 |
0.12 |
3.32 |
0.03 |
0.09 |
0.01 |
Potassium (mg) |
7.05 |
7.49 |
0.36 |
0.40 |
6.45 |
10.25 |
Carb (g) |
0.16 |
0.79 |
0.21 |
0.83 |
0.20 |
0.28 |
Protein (g) |
0.26 |
0.03 |
0.03 |
0.00 |
0.21 |
0.20 |
Vitamin A (%) |
0.00 |
0.00 |
0.00 |
0.00 |
0.01 |
0.08 |
Vitamin B-6 (%) |
0.17 |
0.12 |
0.00 |
0.00 |
0.68 |
0.85 |
Vitamin C (%) |
0.00 |
0.02 |
0.00 |
0.00 |
0.02 |
0.09 |
Iron (%) |
0.25 |
0.09 |
0.07 |
0.03 |
0.29 |
0.21 |
Calcium (%) |
0.09 |
0.05 |
0.00 |
0.00 |
0.07 |
0.10 |
Table below shows the cost of each ingredients per 1 gram:
peanut |
raisin |
pretzel |
dried cranberries |
sunflower seed |
pistachio |
|
cost per 1 gram ($) |
$ 0.005 |
$ 0.020 |
$ 0.013 |
$ 0.013 |
$ 0.022 |
$ 0.031 |
Per marketing department research, each bag of snack should have at least 10 grams of each ingredient. Having this information answer the following questions. Please make sure that the information is easy to read and understand. Dedicate a separate worksheet to each question and order the worksheets by the number of questions.
5 - Quality control team notices that due to measurement errors, there is some uncertainty in measuring the calories level in peanut. They collect a peanut sample of size 35 and measure the calories for each observation as shown in table below.
Observation |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
18 |
19 |
20 |
21 |
22 |
23 |
24 |
25 |
26 |
27 |
28 |
29 |
30 |
31 |
32 |
33 |
34 |
35 |
Calories |
5.21 |
5.45 |
5.37 |
5.12 |
6.84 |
6.38 |
4.46 |
6.46 |
6.55 |
4.8 |
5.46 |
5.72 |
6.71 |
6.5 |
5.74 |
4.75 |
5.95 |
6.73 |
5.35 |
5.75 |
4.6 |
5.33 |
5.8 |
6.21 |
4.74 |
5.39 |
5.6 |
4.57 |
6.7 |
6.18 |
5.9 |
6.3 |
5.41 |
6.84 |
5.1 |
Create a 99% confidence interval of peanut calories. Then using the upper limit and lower limit values of peanut calories recalculate the optimum solution. How much does the uncertainty regarding the peanut calories affect the optimum cost of one bag? Make sure you include all related information about confidence interval. (10 pts)