Other Math Answers

(b) A company is involved in the production of two items (X and Y). The resources need to produce X and Y are twofold, namely machine time for automatic processing and craftsman time for hand finishing. The table below gives the number of minutes required for each item:

Machine time Craftsman time
Item X 13 20
Item Y 19 29

The company has 40 hours of machine time available in the next working week but only 35 hours of craftsman time. Machine time is costed at £10 per hour worked and craftsman time is costed at £2 per hour worked. Both machine and craftsman idle times incur no costs. The revenue received for each item produced (all production is sold) is £20 for X and £30 for Y. The company has a specific contract to produce 10 items of X per week for a particular customer. Formulate the problem of deciding how much to produce per week as a linear program hence make the decision.

Solve the following game

x y
x 2 5
y 4 1

(a) Long Castling Breweries manufactures two brands of beer, Benko lager and Benoni lager. Benko has a contribution of Sh.4 per unit and Benoni has a contribution of Sh.3 per unit. Benko requires 30 machine minutes and 30 labor minutes to manufacture a unit whereas a unit of Benoni requires 20 machine minutes and 30 labor minutes to manufacture. Total available machine hours per day are 12hrs whereas total available labour hours per day are 14hrs.
Required:
i) Formulate linear programming model
ii) How much of each brand should Long Castling produce if it wishes to maximize its daily contribution assuming that all the lager produced is sold

(b) Determine the optimal solution to the transportation problem given below using least cost method(10 marks)
V W X Y Z SUPPLY
A 1 9 13 36 51 50
B 24 12 16 20 1 100
C 14 33 1 23 26 150
DEMAND 100 70 50 40 40

A sum of money is to be divided among Ali, Brent and Carol in the ratio 2:3:5, Carol’s share amounts to $ 1050. Calculate
(A) The total sum of money to be shared
(B) Brent’s share

The depth (D metres) of water in a harbour at a time (t hours) after midnight on a particular day can be modelled by the function
D = 2 times sin times ( 0.51 times t minus 0.4 ) + 5 , em space times t less-than-or-equal 15 ,
where radians have been used.
Select the two options which are correct statements about the predictions based on this model.

Select one or more:
The largest depth is 7 metres.
At midnight the depth is approximately 4.2 metres.
The depth of water in the harbour falls after midnight. 
The model can be used to predict the tide for up to 15 days. 
The time between the two high tides is exactly 12 hours. 
At midday the depth is approximately 7 metres. 
The smallest depth is 5 metres. 

In a supermarket cans of beans are on display. There is one can in the front row, 2 in the second, 3 in the
third, 4 in the forth and so on.
(a) Find how many rows are needed to have at least 24 cans in total on display.
(b) Show that there are no more than 12 cans in the first 4 rows.

56 people go to a party. 24 take food, 12 take drink and 8 take both food and drink. Find the probability of
someone from the party going without food or drink.

) Bob has 4 different coins in his pocket. They add to 28p. He takes two coins out of his pocket and puts one
different coin in. What is the maximum amount he can now have in his pocket?

) Given 2p – 3q = 10, write an expression for the number (a) 100 (b) 30 and (c) -10