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Operations Research
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
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
Operations Research
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?
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?
Operations Research
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?
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?
Operations Research
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?
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?
Operations Research
Given the constraints
A+B + C ≤ 24, B +C ≥ 8 and A ≥ 0, B ≥ 0, C ≥ 0.
Maximize 24-A-B - C
A: amount of time spent on school work
B: amount of time spent on fun
C: amount of time spent on pay work
A+B + C ≤ 24, B +C ≥ 8 and A ≥ 0, B ≥ 0, C ≥ 0.
Maximize 24-A-B - C
A: amount of time spent on school work
B: amount of time spent on fun
C: amount of time spent on pay work
Operations Research
How many types of failures are considered in replacement theory?
Operations Research
Execute the Job Assignment Problem and prove the solution
Operations Research
1.3 Minimize z = a + b + c
Subject to:
1. a - b - c ≤ 0
2. a + b + c ≥ 4
3. a + b - c = 2
4. a, b ≥ 0
Subject to:
1. a - b - c ≤ 0
2. a + b + c ≥ 4
3. a + b - c = 2
4. a, b ≥ 0
Operations Research
How to solve the following linear program using simplex algorithm:
Minimizer z=a+b+c
Subject to 1.a-b-c lesser than or equal to 0
2.a+b+c greater than or equal to 4
3.a+b-c=2
4.a,b greater than or equal to 0
Minimizer z=a+b+c
Subject to 1.a-b-c lesser than or equal to 0
2.a+b+c greater than or equal to 4
3.a+b-c=2
4.a,b greater than or equal to 0
Operations Research
Solve the following linear program using simplex algorithm
Minimize z= a+b+c
Subject to: 1. a - b -c<=0
2. a + b + c>=4
3. a +b-c=2
Minimize z= a+b+c
Subject to: 1. a - b -c<=0
2. a + b + c>=4
3. a +b-c=2
