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Please solve the following system of exponential equations: 1=ae^11b+c
3=ae^9b+c
10=ae^6b+c.
Show all steps and briefly explain the steps as you go.
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18. What is the probability of more than 5 customers arriving at the supermarket check-out counter in a given one hour period?
A. 0.56
B. 0.44
C. 0.38
D. 0.71
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(b) The mesh equations of a circuit are given by
i_1 + 1_2 + 2i_3 = 9
4i_1 + 4i_2 - 3i_3 = 3
5i_1 + i_2 + 2i_3 = 13
Check for diagonal dominance and solve the system of equations using Gauss-Siedel iteration. Perform three iterations with the zero vector and retain four decimal places in your working.
Please solve the following system of exponential equations: 1=ae^11b+c
3=ae^9b+c
10=ae^6b+c.
Show all steps and briefly explain the steps as you go.
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Customers arrive at a supermarket check-out counter following a Poisson distribution with an average arrival rate of 5 customers per hour.
18. What is the probability of more than 5 customers arriving at the supermarket check-out counter in a given one hour period?
A. 0.56
B. 0.44
C. 0.38
D. 0.71
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A certain state is contemplating creating a weekly lottery, the revenues from which will be used to fund improvements in the state’s public education system. The commission chartered to develop the guidelines for the proposed lottery envisions using a process whereby six (6) balls will be randomly selected from a single bin containing a total of forty (40) balls, each of which is individually numbered 1 through 40, in order to determine the winning lottery numbers each week. Once a given ball has been randomly selected it will not be placed back in the bin before selecting the next ball. The commission is currently debating whether an individual should be required to pick the winning lottery numbers in a specific order or be allowed to pick them in a random order.
2. Assuming that the order in which the winning lottery numbers are selected is relevant (i.e., is important), what is probability of someone correctly selecting the six (6) winning lottery numbers?
A. 0.00000000026
B. 0.00000000066
C. 0.00000000036
2. Assuming that the order in which the winning lottery numbers are selected is relevant (i.e., is important), what is probability of someone correctly selecting the six (6) winning lottery numbers?
A. 0.00000000026
B. 0.00000000066
C. 0.00000000036
D. 0.00000000078
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(a) Determine a matrix that shears horizontally by a factor of 2 and then rotates anticlockwise about the origin by 45 degrees. Show graphically the effect of the transformation on the unit square.
(b) The mesh equations of a circuit are given by
i_1 + 1_2 + 2i_3 = 9
4i_1 + 4i_2 - 3i_3 = 3
5i_1 + i_2 + 2i_3 = 13
Check for diagonal dominance and solve the system of equations using Gauss-Siedel iteration. Perform three iterations with the zero vector and retain four decimal places in your working.
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s.t. X1 + X2 – X3 >= 5
X1 - 2X2 + 4X3 >=8
X1, X2, X3 >=0
2 – Use the simplex algorithm to find the optimal solution to the following LP:
Min Z = -4X1 + X2
s.t. 3X1 + X2 <= 6
- X1 + 2X2 <=0
X1, X2 >= 0
3 - A bank has two sites at which checks are processed. Site 1 can process 10,000 checks per day, and site 2 can process 6000 checks per day. The bank processes three types of checks: vendor, salary, and personal. The processing cost per check depends on the site (table below). Each day 5000 checks of each type must be processed. Formulate a balanced transportation problem to minimize the daily cost of processing checks. Only complete formulation needs to be submitted. Do not solve.
Site1 Site2
Vendor checks 5 cents 3 cents
Salary checks 4 cents 4 cents
Personal checks 2 cents 5 cents
1 - Use the dual simplex method to solve the following LP:
Max Z = -2X1 - X3s.t. X1 + X2 – X3 >= 5
X1 - 2X2 + 4X3 >=8
X1, X2, X3 >=0
2 – Use the simplex algorithm to find the optimal solution to the following LP:
Min Z = -4X1 + X2
s.t. 3X1 + X2 <= 6
- X1 + 2X2 <=0
X1, X2 >= 0
3 - A bank has two sites at which checks are processed. Site 1 can process 10,000 checks per day, and site 2 can process 6000 checks per day. The bank processes three types of checks: vendor, salary, and personal. The processing cost per check depends on the site (table below). Each day 5000 checks of each type must be processed. Formulate a balanced transportation problem to minimize the daily cost of processing checks. Only complete formulation needs to be submitted. Do not solve.
Site1 Site2
Vendor checks 5 cents 3 cents
Salary checks 4 cents 4 cents
Personal checks 2 cents 5 cents
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