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Let 𝑀𝑋 (𝑡) = 𝑘𝑒 𝑡 1−0.8𝑒 𝑡 with µ=5 and define 𝑍 = 2𝑋 +3 , find Var(Z).
You are working at a firm that conducts independent testing for heavy industry. Recently, an automobile manufacturer has been in the news for complaints about the highway gas mileage of their latest model minivan. You receive a contract from a consumer action group to test and write a report on the company’s claim that its minivans get 28 miles per gallon on the highway. The car company agrees to allow you to select randomly 35 low-mileage fleet minivans to test their highway mileage. Your test results gave you the following data:
29.7
24.5
27.1
29.8
29.2
27.0
27.8
24.1
29.3
25.9
26.2
24.5
32.8
26.8
27.8
24.0
23.6
29.2
26.5
27.7
27.1
23.7
24.1
27.2
25.9
26.7
27.8
27.3
27.6
22.8
25.3
26.6
26.4
27.1
26.1
Sample Mean, Standard deviation, confidence interval
Calculate a 95% confidence interval around your sample mean. (75 words, or 1 paragraph)
What is the null and alternative hypothesis?
Suppose the average number of calls received by an operator in one minute is 2. What is the probability of receiving 10 calls in 5 minutes ?
For the population of 2,5,4,3,2
Construct the sampling distribution of the mean x of size 3 without replacement
1. Given the following transportation problem:
D1 D2 D3 D4 SS
S1 5 10 7 10 50
S2 9 10 3 3 40
S3 6 4 2 2 60
DD 40 30 10 70
Where D1, D2, D3, and D4 are destinations and the values in the shaded cells are costs;
A. Determine the basic feasible solution through NWCM, LCM and VAM
B. Determine the optimal solution through Stepping Stone and MODI Method
Bedele Brewery produces Ale and Beer. Suppose that the productions are limited by scarce resources of Corn, Hops and Barely malt. To make Ale, 5 kg of Corn, 4 Kg of Hops and 35 Kg of Barely malt are required. To make Beer, 15 Kg of Corn, 4 Km of Hops and 20 Kg of Barely malt are required. Suppose that only 480 Kg of Corn, 160 Kg of Hops and 1190 Kg of Barely malt are available. The Brewery plans to enjoy a Profit of Birr 13 for each Kg of Ale and Birr 23 for each Kg of Beer.
Required:
Formulate the linear programming model
How many Ale and Beer should the Brewery Company produce in order to maximize the returns? Using the graphical method.
What is the total profit?
Is there any slack? Identify
A firm produces products A, B, and C, each of which passes through assembly and inspection departments. The number of person hours required by a unit of each product in each department is given in the following table.
Person hours per unit of product
Product A
Product B
Product C
Assembly
2
4
2
Inspection
3
2
1
During a given week, the assembly and inspection departments have available at most 1500 and 1200 person-hours, respectively. if the unit profits for products A, B, and C are Birr 50, Birr 40, and Birr 60, respectively, determine the number of units of each product that should be produced in order to maximize the total profit and satisfy the constraints of the problem
Bedele Brewery produces Ale and Beer. Suppose that the productions are limited by scarce resources of Corn, Hops and Barely malt. To make Ale, 5 kg of Corn, 4 Kg of Hops and 35 Kg of Barely malt are required. To make Beer, 15 Kg of Corn, 4 Km of Hops and 20 Kg of Barely malt are required. Suppose that only 480 Kg of Corn, 160 Kg of Hops and 1190 Kg of Barely malt are available. The Brewery plans to enjoy a Profit of Birr 13 for each Kg of Ale and Birr 23 for each Kg of Beer.
Required:
Formulate the linear programming model
How many Ale and Beer should the Brewery Company produce in order to maximize the returns? Using the graphical method.
What is the total profit?
Is there any slack?
If ( x*2 +1/x)*2 =15
Then x=1/x=?
let
f(x) =1 + 2𝑥, 𝑥 ≤ 0
=3𝑥 − 2,0 < 𝑥 ≤ 1
= 2𝑥 ଶ − 1, 𝑥 > 1
i) Check whether f is discontinuous. If yes, find where? ii) Give a rough sketch of the graph of f.
#340153 on Dec 2023