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Find the domain of the function defined by f(x) =√(9x³-x⁴)
Given a hypothetical consumption function of the form:
Y = C + I0 + G0
C = α + β
Where: = Y – T
Y = Income
T = Taxes
Compute the equilibrium level of income and consumption (4 marks)

5+55+555.....to n terms
Prove that a non empty finite set S which is a subset of R contains its infimum
If you double the length of the side of a square, by how much do you increase the area of that square?
4. A photocopier in an office is operated by a person who does other jobs also. The average service time for a job is 6 minutes per customer. On average, every 12 minutes one customer arrives for photocopier. Find:
Arrival rate per hour
Service rate per hour
i. The photocopier utilization rate.
ii. Percentage of times that an arrival has not to wait. (2 marks)
The table below gives the proposed prices for two competing airlines

Airline A

Airline B

A1

A2

A3

A4

B1
B2
B3
B4
0.12
-0.23
0.59
-0.05
0.61
0.28
0.19
-0.21
0.18
0.19
0.17
0.01
0.41
0.53
0.13
0.03
Required:
i. Determine the mixed strategies (4 marks)
Calculate the value of the game.
The failure rates of 1000 street bulbs in a town are summarized in the table below:
End of Month
1
2
3
4
5
6
Probability of failure to date
0.05
0.20
0.40
0.65
0.85
1.0
The cost of replacing an individual bulb is Sh. 60. If all the bulbs are replaced simultaneously it would cost Sh. 25 per bulb. Any one of the following two options can be followed to replace the bulbs:-
i. Replace the bulbs individually when they fail (individual replacement policy)
ii. Replace all the bulbs simultaneously at fixed intervals (Group replacement policy)
Find out the optimal replacement policy? If group policy is optimal, find at what equal intervals should all the bulbs be replaced?
A manufacturing company needs 2500 units of a particular component every year. The company buys it at the rate of Sh. 30 per unit. The order processing cost for this part is estimated at Sh. 15 and the cost of carrying a part in stock comes to about Sh.4 per year. The company can manufacture this part internally. In that case, it saves 20% of the price of the product. However, it estimates a set-up cost of Sh. 250 per production run. The annual production rate would be 4800 units. However, the inventory holding costs remain unchanged.
i. Determine the EOQ and the optimal number of orders placed in a year. (3 marks)
ii. Determine the optimum production lot size and the average duration of the production run. (4 marks)
iii. Should the company manufacture the component internally or continue to purchase it from the supplier? (5 marks)
If 3% of the fruits brought into the market are over ripe, find the probability that 5 are over ripe in a sample of 100 fruits
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