STAT201 Week sales data for a Kashmiri tea house comprising
Mathematics
Solve the following questions.
- The following is the 8 week sales data for a Kashmiri tea house comprising the number of customers (in hundreds) and weekly sales (in thousand SRs).
- In a simple regression model study, the following results arefound:
- Two advertising media are being considered for promotion of a product. Website ads cost SAR 300 each, while TV ads cost SAR 500 each. The total budget is SAR 4000 per week. The total number of ads should be at most 15, with at least 5 of each type. Each TV ad reaches 800 people, while each Website ad reaches 500 people. The company wishes to (find the number of ads of each type to be placed) to reach as many people as possible while meeting all the constraints stated. Formulate this problem as an LPP.
- Solve the following Linear Programming graphically
|
No of Customers |
15 |
9 |
40 |
20 |
25 |
25 |
15 |
35 |
|
Weekly Sales |
06 |
04 |
16 |
06 |
13 |
09 |
10 |
16 |
- Find the simple linear regression equation of weekly sales over number of customers.
- What will be sales of ninth week given that the average number of customers is 30?
and, . Compute SSE.
3.A new shopping mall is considering setting up an information desk manned by one employee. Based on information obtained from similar information desks, it is believed that people will arrive at the desk at the rate of 20 per hour. It takes an average of 2 minutes to answer a question. It is assumed that arrivals are Poisson and answer times are exponentially distributed.
a.Find the probability that the employee is idle.
b.Find the average number of people receiving and waiting to receive information.
c.Find the average time a person seeking information spends at the desk.
4.A university cafeteria line in the student center is a self-serve facility in which students select the food items they want and they form a single line to pay the cashier. Student arrive at cashier at the rate of about three per minute according to a Possion distribution. The single cashier ringing up sales takes about 15 seconds per customers, following an exponential distribution.
- What is the expected number of students in the queue?
- How long will the average student have to wait before reaching the cashier?
Max Z = 50x + 18y
Subject to:2 x + y ≤ 100
x + y ≤ 80
andx, y ≥ 0.
