Math Answers

QUESTION THREE

A poultry farmer in Lufyanyama has obtained a loan from the Bank to boost his poultry

business. He provides you with data to help him optimize the sales. The data is that Old

hens can be bought for K2 each but young one cost K5 each. The old hens lay 3 eggs

per week and young ones 5 eggs per week, each egg being worth 30ngwee. A hen cost

K1 per week to feed. If a person has only K80 to spend on hens, how many of each kind

should he buy to get a profit of more than K6 per week assuming that he can’t house

more than 20 hens?

a)Formulate the problem as a linear programming model [8 Marks]

b)Using the graphical method procedure, how many hens should he buy of each kind to

maximize the profit per week? [10 Marks]

c) Determine the ranges of optimality for the objective function coefficients

A manufacturer knows that on average 20% of the electric toasters produced require repairs

within 1 year after they are sold. When 20 toasters are randomly selected, find appropriate numbers x

and y such that

(a) the probability that at least x of them will require repairs is less than 0.5;

(b) the probability that at least y of them will not require repairs is greater than 0.8.

Determine whether the argument is valid or invalidusing critical row.

a. 𝑝⋁~𝑞

𝑞 over ∴𝑝

b. 𝑝→~𝑞

𝑞 over ∴~𝑝

Instruction: Write each statement in symbolic form and determine whether the argument is valid or invalid using critical row

.

a. If Caroline is late (l), we will not pursue our plan (~p). We did not pursue our plan. Therefore, Caroline was late.

b. If you are Mathematician (m), then you are logical (l). You are mathematician. Therefore, you are logical.

c. He will attend PLM (p) or UP (u). He did not attend UP. Therefore, he attended PLM.

Let the function , defined by

f(x)= 1/x+3 ; x∈ [3,∞[

Check whether f is uniformly continuous or not on the interval of definition