Other Math Answers

Player R has a $2, a $5, and a $10 bill. Player C has a $1, a $5, and a $10 bill. Each player selects and shows (simultaneously) one of his or her three bills. If the total value of the two bills shown is even, R wins C’s bill; if the value is odd, C wins R’s bill. (Which player would you rather be?)

(A)Set up the payoff matrix for the game.
(B)Solve the game using the simplex method discussed in this section. (Remove any recessive rows and columns, if present, before you start the simplex method.)

A company produces two brands of trail mix, regular and deluxe, by mixing dried fruits, nuts, and cereal. The recipes for the mixes are given in the table. The company has 1,200 pounds of dried fruits, 750 pounds of nuts, and 1,500 pounds of cereal to be used in producing the mixes. The company makes a profit of $0.40 on each pound of regular mix and $0.60 on each pound of deluxe mix. How many pounds of each ingredient should be used in each mix in order to maximize the company’s profit?

Type of mix: - Ingredients:
Regular - At least 20% nuts
At most 40% cereal
Deluxe - At least 30% nuts
At most 25% cereal

1. add the following 8-bit binary numbers .

i. (01001110)2 + (00111100)2

ii.(10011101)2 + (10001111)2

(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