I can upload you the file if needed since charts are hard to copy and paste on here Healthy Snacks Co. produces snack mixes.

I can upload you the file if needed since charts are hard to copy and paste on here

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:

peanutraisinpretzeldried cranberriessunflower seedpistachioCalories5.673.001.003.085.845.62Fat (g)0.490.000.010.010.510.06Sodium (mg)0.180.123.320.030.090.01Potassium (mg)7.057.490.360.406.4510.25Carb (g)0.160.790.210.830.200.28Protein (g)0.260.030.030.000.210.20Vitamin A (%)0.000.000.000.000.010.08Vitamin B-6 (%)0.170.120.000.000.680.85Vitamin C (%)0.000.020.000.000.020.09Iron (%)0.250.090.070.030.290.21Calcium (%)0.090.050.000.000.070.10

Table below shows the cost of each ingredients per 1 gram:

peanutraisinpretzeldried cranberriessunflower seedpistachiocost 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.

1 - Formulate a LP for Healthy Snacks to minimize total cost of producing one bag of snack while satisfying all constraints. Clearly state your decision variables, objective function and constraints. 

2 - Use Excel Solver to solve the formulated LP and find the optimum values of each ingredient that should be included in the snack bag as well as optimum cost of one bag. 

3 - Healthy Snacks decides to change its pistachio supplier. However, the procurement team believe that the pistachio supplied by the new supplier has a different level of Vitamin A. To test this, they collect a pistachio sample size of 25 and measure the Vitamin A level. Table below shows the vitamin A level in each observation of the sample per 1 gram:

Observation12345678910111213141516171819202122232425Vitamin A (%)0.1150.1260.1340.1030.1150.0960.0990.0780.1140.1110.1190.1110.0810.1010.1210.0880.1170.1020.1030.1070.1260.1300.0770.1170.123

Conduct a hypothesis test at 5% significance and check if the vitamin A level in the new supplier pistachio is different from the current level. If yes, how should the company change the mix of ingredients in its snack bag in order to minimize the cost of one bag (consider the average vitamin A level in the new supplier sample)? Is the new bag cheaper or more expensive? Make sure you include all related information such p-value and test statistic in your answer. 

4 - In the original problem (before changing the pistachio supplier), can the company produce a snack bag with calories <= 700? If yes, how much more expensive this new bag would be if optimized for cost compared to the original problem? If no, why do you think it is not possible? 

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.

Observation1234567891011121314151617181920212223242526272829303132333435Calories5.215.455.375.126.846.384.466.466.554.85.465.726.716.55.744.755.956.735.355.754.65.335.86.214.745.395.64.576.76.185.96.35.416.845.1

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. 

6 - Assume the cost of ingredients can change up to 20%. That means each ingredient may be purchased at their original cost +/- 20%. How much does this change may affect the optimum solution. To answer this question, solve the LP problem while changing the cost of one ingredient by +/- 20% and keep the other ingredients' costs at their original value. So for each ingredient, you need to calculate two optimum solutions. Create a bar chart where each column shows an ingredient and each ingredient has two columns. One for +20% change optimum cost and one for -20% optimum cost. To which ingredient do you think the optimum solution is most sensitive? That is the variation in which ingredient causes the most change in the optimum solution? 

7 - While we assume the principle of certainty, in reality, the coefficients of constraints or the objective function in a LP are subject to changes. Dried cranberries calories is assumed to be 3.08. However, this value can change for different batches of dried cranberries. Assume that dried cranberries calories is a uniform random variable in the interval [2.4, 3.4]. Generate 30 random numbers in the interval [2.4, 3.4]. For each random number generated solve the LP once considering the random number to be the dried cranberries calories. Out of 30 times that you solved the LP problem, what percentage of times were you not able to find an optimum solution due to infeasibility? Create a 95% confidence interval for this percentage. Note that the calculated infeasibility percentage is p_bar. What does this practice tell you about LP limitations? Make sure you include all related information such as test statistic in your answer.

8 - Increase the right hand side (RHS) of total calories constraint from 800 to 820 by increments of 1. Each time that you change the RHS, solve the problem and record the optimum cost. Create a line chart that shows the RHS on the x axis and optimum cost on y axis. Can we change the optimum cost by increasing the RHS as much as we want? Or there is a limitation in improving the cost by increasing the RHS? Why? 

9 - Healthy Snacks decides to change its pretzels supplier. In the review process, they limit their options to four suppliers. Except Sodium level, every other specification of pretzels produced by the four suppliers is the same. Table below lists the sodium level in pretzels obtained by sampling the products of each supplier.

No.Supplier 1Supplier 2Supplier 3Supplier 412.933.093.383.3623.182.733.033.3433.052.702.533.6843.342.912.583.7052.682.822.673.3362.922.682.543.4272.913.032.713.4582.632.962.793.2592.902.842.513.42103.282.373.263.75112.552.442.582.98123.152.783.113.12133.092.862.533.35142.942.282.443.72152.842.722.792.93

Is there any significant difference between the sodium level of pretzels produced by each supplier considering α=0.05

? If yes, which supplier(s) would you pick in order to minimize the cost of one bag of snack? Make sure you include all related information such p-value and test statistic in your answer.