Question 1

a. 1,200 parts arrived from a manufacturer in two batches. Each unit of the first batch cost $37, while each unit of the second batch cost $35. If the total cost is $43,600, how many units were in each batch?

b. A furniture factory manufactures two types of coffee tables, A and B. Each table goes through two distinct costing stages, assembly and finishing. The maximum capacity for assembly is 195 hours and for finishing, 165 hours. Each A table requires 4 hours assembly and 3 hours finishing, while a B table requires 1 hour for assembly and 2 hours of finishing. Calculate the number of A and B tables to be produced to ensure that the maximum capacity available is utilized.

Question 2

A company determines that Q units of its products can be sold daily at a price of P= (200 - Q) cedis. The cost of producing Q units per day is C (Q) +2Q.

Find

1. the production level that maximizes revenue The maximum revenue.
2. The production level that maximizes profit.
3. The price per unit that should be charged in order to obtain maximum profit.

Question 3

a. Distinguish between discrete and continuous data.

b. As part of a marketing exercise your firm has collected the following data on the population of a small town

Age	No of Persons
0-5	9
5-15	61
15-30	92
30-45	69
45-65	100
65-75	20
75 and Over	2

i. Find the mean age of the population

ii. Find the standard deviation of the population?s age

iii. Draw a histogram for the distribution of the ages and use your diagram to estimate the modal age of the population.

iv. What is the median age of the population?

c. Given that P(AUB).8 and P(A).3, find P(B) if events A and B are:

i. Mutually exclusive

ii. Independent

Question 4

1. A firm manufacturing two types of switching modules, A and B, is under contract to produce a daily output of at least 35 modules in all. Assembly and testing times for each module are as follows:

Module type	Processing time (hours)
Assembly	Testing
A	1.0	2.0
B	2.0	1.0

Available staff resources provide a daily maximum of 80 hours for assembly and 55 hours for testing. The profit on the sale of each A-module is GHS4.00 and of each B-module is GHS5.00. By using the graphical approach, determine

1. the daily production schedule for maximum profit
2. the maximum daily profit. Question 5 a. Events A, B, and C represent potential member segmentation of customers of a supermarket chain. Events A and B are mutually exclusive and B and C are independent. Given that P (A) .3, P (B) .4, P(C) .5 and P (AUN) .6, find: i. P(B?C) ii. P(BUC) iii. P(AUB) iv. P(A?C ) d. Three machines A, B and C produce 50%, 40% and 10% respectively of the total production. Their respective percentage of defective production are 2%, 2% and 5% for machines A, B and C. i. If an item is selected at random from the collective output of the machines, find the probability that it is defective. ii. If two items are selected at random from the collective output, find the probability that at least one of them is defective iii. Given that a defective item is selected, what is the probability that it is produced by machine C.?

Question 1 a. 1,200 parts arrived from a manufacturer in two batches. Each unit of the first batch cost $37, while each unit of the second batch cost $35. If the total cost is $43,600, how many units were in each batch? b. A furniture factory manufactures two types of coffee tables, A and B. Each table goes through two distinct costing stages, assembly and finishing. The maximum capacity for assembly is 195 hours and for finishing, 165 hours. Each A table requires 4 hours assembly and 3 hours finishing, while a B table requires 1 hour for assembly and 2 hours of finishing. Calculate the number of A and B tables to be produced to ensure that the maximum capacity available is utilized. Question 2 A company determines that Q units of its products can be sold daily at a price of P= (200 - Q) cedis. The cost of producing Q units per day is C (Q) =400+2Q. Find i. ii. iii. the production level that maximizes revenue The maximum revenue. The production level that maximizes profit. The price per unit that should be charged in order to obtain maximum profit. Question 3 a. Distinguish between discrete and continuous data. b. As part of a marketing exercise your firm has collected the following data on the population of a small town Age 0-5 5-15 15-30 30-45 45-65 65-75 75 and Over No of Persons 9 61 92 69 100 20 2 i. Find the mean age of the population ii. Find the standard deviation of the population's age iii. Draw a histogram for the distribution of the ages and use your diagram to estimate the modal age of the population. iv. What is the median age of the population? c. Given that P(AUB)=0.8 and P(A)=0.3, find P(B) if events A and B are: i. Mutually exclusive ii. Independent Question 4 a. A firm manufacturing two types of switching modules, A and B, is under contract to produce a daily output of at least 35 modules in all. Assembly and testing times for each module are as follows: Module type A B Processing time (hours) Assembly Testing 1.0 2.0 2.0 1.0 Available staff resources provide a daily maximum of 80 hours for assembly and 55 hours for testing. The profit on the sale of each A-module is GHS4.00 and of each B-module is GHS5.00. By using the graphical approach, determine i. ii. the daily production schedule for maximum profit the maximum daily profit. Question 5 a. Events A, B, and C represent potential member segmentation of customers of a supermarket chain. Events A and B are mutually exclusive and B and C are independent. Given that P (A) =0.3, P (B) =0.4, P(C) =0.5 and P (AUN) =0.6, find: i. P(BC) ii. P(BUC) iii. P(AUB) iv. P(AC ) d. Three machines A, B and C produce 50%, 40% and 10% respectively of the total production. Their respective percentage of defective production are 2%, 2% and 5% for machines A, B and C. i. If an item is selected at random from the collective output of the machines, find the probability that it is defective. ii. If two items are selected at random from the collective output, find the probability that at least one of them is defective iii. Given that a defective item is selected, what is the probability that it is produced by machine C