Linear Programming is a mathematical method used to allocate scarce resources. It is a technique used to optimize the value of some objective when the factors so involved are subject to some constraints. (kindly use the comment box below to ask a question).

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The mathematical representation of what is expected to achieve is called the Objective Function. The limited resources which may hinder the possible realization of the objectives is called the Constraints and the general limitation in respect of all maximizing problem which states that it is impossible to get negative quantities of a product are called Non-negativity Constraints.

Linear Programming Questions

1. Solve graphically

Maximize 13x₁ + 15x₂

Subject to:

2x₁ + x₂  50      x_{1 ≤} 18

2x₁ + x₂  90      x_{2 ≥} 8

x₁ + x₂  30        x_{2  ≥} 0

2. Minimize 160x + 150y

Subject to:

2x + 3y _≥ 150

X + 4y _≥ 400

5x + 2x_≥  100

X ≥ 0, y _≥ 0

3. HerMAJESTY Nigeria Ltd. Produces two types of bricks “Hard” and “SOFT”. The contribution to profit is N500 and N400 respectively. The bricks have to pass through three departments during production. The labor hours required and available for each product in each department is given in the table below:

(kindly rotate your phone to view the table below)

PRODUCT	MIXING	PACKING	MOLDING
Hard	10	3	2
Soft	5	2	3
Maximum hours available	800	300	60

• Formulate a linear programming model.
• How many units of each product should be produced to maximize profit?

4. SoftStudyNg.com produces two types of software say X and Y. The raw materials constraints for X and Y are:

3x + 4y < 270

6x + 5y ≤ 600

The profit margin per unit for type X is N80.00 while that of type Y is N120.00. What should be the production plan that will maximize the profit? What is the maximum contribution?

5. Ify Catering services have 150gms, 100gms, and 1800gms of rice, meat and fish respectively. Ify requires 150gms of rice and 100gms of each of fish and meat to make a plate of ordinary rice. She also requires 200gms of rice, 150gms of fish and 100gms of meat to make a plate of fried rice. If she sells a plate of fried rice for N50 and a plate of fried rice for N70, find how many plates of each she should make to maximize the sales.

6. Kings Manufacturing Company produces 100kg of a product with at least 60% of type X and 20% of type Y. He can use two materials X which cost N30.00 per kilogram yielding 40% of X and 40% of Y and Y cost N40.00 per kilogram yielding 30% of X and 60% of Y. Find by a graphical method the mix of X and Y to yield the minimum material cost production.

7. Richard plc. Makes two types of biscuit x₁ and x₂ each of which requires passing through three sections of the production; mixing, heating, and packing. The number of hours required to complete each process for a unit of the biscuit is given below:

(kindly rotate your phone to view the table below)

	MIXING	HEATING	PACKING
X1	120	50	150
X2	100	150	50

The hours available for each of the section is 480 hours. If the contribution to profit of x₁ is N850 and x₂ is N800; find:

• The objective function.
• The constraint inequalities.
• The number of x₁ and x₂ to be produced in order to maximize profit.
• The maximum profit.

8. Solve graphically:

Minimize    z = 0.3x + 0.45y

Subject to:

X + Y ≥ 10

X – Y ≥ 0

2x + 3x ≤ 30

X ≥ 0, Y ≥ 0

Other Mathematics Questions

1. Co-ordinate Geometry
2. Permutation and Combination
3. Set Theory
4. Empirical Probability
5. Integration & Vector Algebra
6. Differentiation

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