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Write the dual of the following LPP after reducing it to canonical form.
Min Z = 3x1 + 4x2 + 3x3
Subject to
2x1+4x2 =12
5x1+3x3 ≥11
6x1+ x2 ≥ 8
x1,x2,x3≥0
Solve the following LPP by the two-phase simplex method.
Max Z = x1 + x2 − x3
Subject to
4x1 + x2 + x3 = 4
3x1 + 2x2 - x4 = 6
x1,x2,x3 ≥ 0
Solve the (4x3) game with pay off matrix.
8 5 8
[A] = 8 6 5
7 4 5
6 5 6
At each stage, clearly explain the steps involved.
Which statements about linear programming are true?
There is more than one correct answer. Select all correct answers.
- Linear programming involves values represented by quadratic equations.
- A computer or computational tool is required to solve linear programming problems.
- Constraints are a component of linear programming problems.
- Linear programming is a theoretical method and cannot be shown graphically.
- Linear programming is a method to achieve the best outcome of a situation.
- Linear programming is a special type of optimization.
(more than one answer)
Solve using dual simplex method
Minimize z 2x₁ + 2x₂ + 4x3
2x+3x2 + 5x3 2 2
Subject to 3x1 + x₂ + 7x3 <3
x1 + 4x₂ + 6x3 ≤ 5
A company that produces two kinds of office 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. cOMPUTE THE DUAL PRICE.
The following payoff matrix describes the increase in market share for L.G Company and decrease in market share for Samsung Company:
Company
L.G
Samsung
Strategy
Low advt.
High advt.
Low advt.
4
-6
High advt.
-12
-10
By using Games theory, answer the following points: ∙ Game strategy is considered as:
∙ Saddle point will be:
∙ Game value will be:
∙ Game result is for:
A furniture company manufactures dining room tables and chairs. The company has 150 hours of assembly time available per week and workers must spend at least 100 hours on finishing per week. A table requires 540 minutes for assembly and 180 minutes for finishing. A chair requires 150 minutes for assembly and 60 minutes for finishing. Each table is sold for R4 000 and each chair for R1 500. If x is the number of tables and y the number of chairs produced per week, the constraints and the objective function of the company are [1] 2,5x + y ≥ 1 500; 9x + 3y ≤ 4 000; x, y ≥ 0; π = 150x + 100y. [2] 9x + 2,5y ≥ 150; 3x + y ≤ 100; x, y ≥ 0; T C = 4 000x + 1 500y. [3] 9x + 2,5y ≤ 150; 3x + y ≥ 100; x, y ≥ 0; T R = 4 000x + 1 500y. [4] 540x + 150y ≥ 150; 180x + 60y ≤ 100; π = 4x + 1,5y.
Southern Sporting Goods Company makes basketballs and footballs. Each product is produced from two resources—rubber and leather. The resource requirements for each product and the total resources available are as follows:
Each basketball produced results in a profit of $12, and each football earns $16 in profit.
Formulate a linear programming model to determine the number of basketballs and footballs to produce in order to maximize profit.
Transform this model into standard form.
Solve the model formulated for Southern Sporting Goods Company graphically.
Identify the amount of unused resources (i.e., slack) at each of the graphical extreme points.
This pandemic, Abheedette learned to bake while on home quarantine. She
also realized that she will be able to make P60.00 profit per tray of banana muffins and
P120.00 profit per tray of blueberry muffins. She needs 2 cups of milk and 3 cups of flour
to bake a tray of banana muffins. And, baking a tray of blueberry muffins takes 4 cups
of milk and 3 cups of flour. She has 16 cups of milk and 15 cups of flour. How many trays
of each flavor must be baked to maximize the profit?
a. Define the variable used
b. LP Model
c. Identify the feasible region
d Corner Points and the objective functions
e. Optimal Solution (final answer)
#340153 on Dec 2023