Problem 1: For the following linear programming problem: ???????? ? = 40?1 + 50?2

Subject to constraints:

3?1 − 6?2 ≥ 30

?1 – 15 ≤ 3?2 2

?1 + 3 ?2 = 24

?1, ?2 ≥ 0

1- Find the optimal solution using graphical solution corner points method or iso profit line method. Please, show the values for state variable, decisions variables, and slack and surplus variables

2- Determine the value for basic solution and non-basic solution, binding constraints and nonbinding constrains, and if there are any redundant constraints

3- Identify if there is any special case solution and state it.

solve using linear programming graphical solution

In a team of 50 people, 20 pilots are under 40 years old. 15 pilots are over 40 years old. Five of the non-pilots are under the age of 40, the rest are over the age of 40. Find the probability of being a pilot or over 40 when a random person is selected.

It sampled 40 customers in San Francisco and 50 customers in San Diego to assess potential demand.

On a scale of 1-7 (7 = very likely to buy), San Diego customers had a mean of 3.5 with a standard deviation of 1.1. SF customers had a mean of 4.1 with a standard deviation of 2.3.

Are these markets statistically different?

1.Compute standard error

2.Compute t-calc  

3.Compare |t-calc| to 1.96 (95% confidence in our results) and 2.58 (99% confidence)

4.If |t-calc| > 1.96, reject the null with 95% confidence

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Standard error for 2 means (sxs_x ̅ ) = ?12?1+?22?2√((s_1^2)/n_1 +(s_2^2)/n_2 )

T-calc for 2 means = ?1−?2??(x ̅_1-x ̅_2)/s_x ̅

1500 pound per hour of a waste mixture of 40% benzene, 50% toluene and 10% of water is burned with 25% excessive air. Determine the total heat released and the percent by volume of each component in the flue gas.
thank you.

The project to obtain charitable donations is now 40 days into a planned 50-day project. The project is divided into 3 activities. The first activity is designed to solicit individual donations. It is scheduled to run the first 35 days of the project and to bring in $25,600. Even though we are 40 days into the project, we still see that we have only 92% of this activity complete. The second activity relates to company donations and is scheduled to run for 40 days starting on day 5 and extending through day 45. We estimate that even though we should have (35/40) 88% of this activity complete, it is actually only 52% complete. This part of the project was scheduled to bring in $150,600 in donations. The final activity is for matching funds. This activity is scheduled to run the last 10 days of the project and has not started. It is scheduled to bring in an additional $51,200. So far $177,000 has actually been brought in on the project.

Calculate the schedule variance, schedule performance index, cost variance and cost (actually value in this case) performance index.

What is the:

Schedule variance     $

Schedule performance index

Cost variance $

Cost performance index

1A) Twenty laboratory mice were randomly divided into two groups of 10. Each group was fed according to a prescribed diet. At the end of 3 weeks, the weight gained by each animal was recorded. Do the data in the following table justify the conclusion that the mean weight gained on diet B was greater than the mean weight gained on diet A, at the α = 0.05 level of significance? Assume normality. (Use Diet B - Diet A.)

(a) Find t. (Give your answer correct to two decimal places.)


(b) Find the p-value. (Give your answer correct to four decimal places.)

1B) A bakery is considering buying one of two gas ovens. The bakery requires that the temperature remain constant during a baking operation. A study was conducted to measure the variance in temperature of the ovens during the baking process. The variance in temperature before the thermostat restarted the flame for the Monarch oven was 2.2 for 23 measurements. The variance for the Kraft oven was 3.2 for 21 measurements. Does this information provide sufficient reason to conclude that there is a difference in the variances for the two ovens? Assume measurements are normally distributed and use a 0.02 level of significance.

(a) Find F. (Give your answer correct to two decimal places.)


(b) Find the p-value. (Give your answer correct to four decimal places.)

2. To raise awareness of its capabilities, FedEx developed a sales promotion that was sent to selected offices. To assess the possible benefit of the promotion, FedEx pulled the shipping records for a random sample of 50 offices that received the promotion and another random sample of 75 that did not and collected data on the number of mailings. They want to see if those who received the sales promotions shipped more mailings. The complete set of results is provided below (promotions columns). a. State the null and alternate hypotheses. b. Run the test. Paste the test output and state your decision (minitab - Stat-paired T-Test and CI). c. What is the best estimate for the population difference in means for the number of mailings between offices with the promotion and offices without the promotion? (Be 90% confident in your estimate for the confidence interval). d. Interpret the confidence interval in part c. e. What is the margin of error associated with 90% confidence interval?

Promotion   Mailings
Promotions_NO   15
Promotions_NO   49
Promotions_NO   42
Promotions_NO   22
Promotions_NO   26
Promotions_NO   35
Promotions_NO   38
Promotions_NO   13
Promotions_NO   35
Promotions_NO   14
Promotions_NO   5
Promotions_NO   64
Promotions_NO   27
Promotions_NO   57
Promotions_NO   50
Promotions_NO   43
Promotions_NO   32
Promotions_NO   39
Promotions_NO   13
Promotions_NO   19
Promotions_NO   47
Promotions_NO   45
Promotions_NO   38
Promotions_NO   59
Promotions_NO   35
Promotions_NO   8
Promotions_NO   10
Promotions_NO   58
Promotions_NO   44
Promotions_NO   9
Promotions_NO   10
Promotions_NO   0
Promotions_NO   42
Promotions_NO   37
Promotions_NO   23
Promotions_NO   12
Promotions_NO   54
Promotions_NO   41
Promotions_NO   36
Promotions_NO   43
Promotions_NO   45
Promotions_NO   18
Promotions_NO   65
Promotions_NO   10
Promotions_NO   17
Promotions_NO   59
Promotions_NO   26
Promotions_NO   18
Promotions_NO   8
Promotions_NO   14
Promotions_NO   74
Promotions_NO   29
Promotions_NO   60
Promotions_NO   19
Promotions_NO   30
Promotions_NO   29
Promotions_NO   12
Promotions_NO   0
Promotions_NO   20
Promotions_NO   31
Promotions_NO   13
Promotions_NO   5
Promotions_NO   7
Promotions_NO   42
Promotions_NO   36
Promotions_NO   9
Promotions_NO   23
Promotions_NO   70
Promotions_NO   28
Promotions_NO   25
Promotions_NO   26
Promotions_NO   24
Promotions_NO   50
Promotions_NO   7
Promotions_NO   0
Promotions_YES   38
Promotions_YES   74
Promotions_YES   18
Promotions_YES   65
Promotions_YES   60
Promotions_YES   51
Promotions_YES   71
Promotions_YES   47
Promotions_YES   29
Promotions_YES   39
Promotions_YES   45
Promotions_YES   36
Promotions_YES   57
Promotions_YES   36
Promotions_YES   12
Promotions_YES   20
Promotions_YES   23
Promotions_YES   79
Promotions_YES   16
Promotions_YES   4
Promotions_YES   62
Promotions_YES   37
Promotions_YES   2
Promotions_YES   23
Promotions_YES   6
Promotions_YES   10
Promotions_YES   28
Promotions_YES   65
Promotions_YES   25
Promotions_YES   86
Promotions_YES   27
Promotions_YES   58
Promotions_YES   33
Promotions_YES   54
Promotions_YES   40
Promotions_YES   92
Promotions_YES   71
Promotions_YES   0
Promotions_YES   77
Promotions_YES   60
Promotions_YES   56
Promotions_YES   38
Promotions_YES   16
Promotions_YES   89
Promotions_YES   62
Promotions_YES   9
Promotions_YES   42
Promotions_YES   73
Promotions_YES   49
Promotions_YES   14