Operations Research Answers

A company manufactures two kinds of ice-cream. The vanilla ice-cream sells for $2.50 each while the chocolate flavour ice-cream sells for $4.50 cents each. It costs the company 1 labour hour to make the vanilla flavour ice-cream and 2 labour hours to make the chocolate flavour ice-cream. The company has a total of 300 labour hours available. It costs the company 3 machine hours for the vanilla ice-cream and 2 machine hours for the chocolate ice-cream. The company has a total of 480 machine hours available. How much of each type of ice-cream should the company produce to maximise revenue? What is the maximum revenue? [Hint: let vanilla ice-cream = x]

Two kinds of ice-cream. The vanilla ice-cream sells for $2.50 each while the chocolate flavour ice-cream sells for $4.50 cents each. It costs the company 1 labour hour to make the vanilla flavour ice-cream and 2 labour hours to make the chocolate flavour ice-cream. The company has a total of 300 labour hours available. It costs the company 3 machine hours for the vanilla ice-cream and 2 machine hours for the chocolate ice-cream. The company has a total of 480 machine hours available. How much of each type of ice-cream should the company produce to maximise revenue? What is the maximum revenue?

For the following LP problem, graph the region of feasible solution and solve by the corner-point method.

Maximize z = 5x1 + 8x2
Subject to x1 + x2 ≥ 6
3x1 + 2x2 ≤ 30
2x1 + x2 ≤ 5
x1 , x2 ≥ 0

Check whether the following sets are convex or not: i) S1 = {( x, y)| y - 3 ≤ -(x^2), x ≥ 0, y ≥ 0}
ii) S2 = {(x, y)| y - 3 ≥ -(x^2), x ≥ 0, y ≥ 0}

Given the constraints
A+B+C<or=24,B+C>or=8and A>or=0,C>or=0.
Maximize24-A-B

A:amount of time spent on schoolwork
B:amount of time spent on fun
C: amount of time spent on pay work

Q1. In Zenith Bank, there are five teller points attending to customers for their deposits and withdrawals. The arrival rate is 160 customers in 8 hours. Each teller point spends an uneven amount of time servicing the arrivals which have been observed to have exponential distribution. The average service time is 10 minutes. You are required to determine:

a. The average queue length
b. Average number of customers in the system
Q2. Consider the payoff table below (The payoff in millions of shillings and P S( j ) the probability of state of nature Sj occurring)

Action S1 S2 S3
D 20 25 -10
D 30 15 30
D 40 0 50
Recommend the best decision alternative using
a) Optimistic approach
b) Pessimistic approach

A supermarket organization buys in a particular foodstuff from four suppliers A B,C and D and subjects samples of this to regular tasting tests by expert panels.various characteristics are scored and the total score for the product is recorded. Four tasters a,b,c and d at four sessions obtained the results below. Analayse and comment on these.
Taster a
Session 1 : A 21
Session 2: B 20
Session 3: C 20
Session 4 : D 32

Taster b
Session 1: B 17
Session 2 : D 22
Session 3: A 24
Session 4: C 21

Taster c
Session 1: C 18
Session 2: A 23
Session 3: D 22
Session 4: B 22

Tester d
Session 1: D 20
Session 2: C 19
Session 3: B 19
Session 4: A 26

3. A farmer plans to mix two types of food to make a mix of low cost feed for the
animals in his farm. A bag of food A costs $10 and contains 40 units of
proteins, 20 units of minerals and 10 units of vitamins. A bag of food B costs
$12 and contains 30 units of proteins, 20 units of minerals and 30 units of
vitamins. How many bags of food A and B should the consumed by the
animals each day in order to meet the minimum daily requirements of 150
units of proteins, 90 units of minerals and 60 units of vitamins at a minimum
cost?

2. A company produces two types of tables, T1 and T2. It takes 2 hours to
produce the parts of one unit of T1, 1 hour to assemble and 2 hours to
polish.It takes 4 hours to produce the parts of one unit of T2, 2.5 hour to
assemble and 1.5 hours to polish. Per month, 7000 hours are available for
producing the parts, 4000 hours for assembling the parts and 5500 hours for
polishing the tables. The profit per unit of T1 is $90 and per unit of T2 is $110.
How many of each type of tables should be produced in order to maximize the
total monthly profit?

1. A store sells two types of toys, A and B. The store owner pays $8 and $14 for
each one unit of toy A and B respectively. One unit of toys A yields a profit of
$2 while a unit of toys B yields a profit of $3. The store owner estimates that
no more than 2000 toys will be sold every month and he does not plan to
invest more than $20,000 in inventory of these toys. How many units of each
type of toys should be stocked in order to maximize his monthly total profit
profit?