Linear Programming Calculator

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**Step 2 :**

**Step 3 :**

Linear programming deals with the optimization (maximization or minimization) of linear functions subject to linear constraints. Linear Programming Calculator is a tool which makes calculations easy and fun. Try our Free Linear Programming Calculator and get your problems solved instantly.

You can see a default objective function along with the linear inequalities and set of constraints given below. The calculator will solve the inequalities and find the coordinates and mark the feasible region. And finally find the value of objective function when on clicking "Submit".

You can see a default objective function along with the linear inequalities and set of constraints given below. The calculator will solve the inequalities and find the coordinates and mark the feasible region. And finally find the value of objective function when on clicking "Submit".

Identify the unknowns in the given LPP. Denote then by x and y then formulate the objective function in terms of x and y. be sure whether it is to be maximized or minimized.

Translate all the constraints in the form of linear inequations.

Solve these inequations simultaneously. Mark the common area by shaded region which will be the feasible region and now find the coordinates of all the vertices of the feasible region

Find the value of the objective function at each vertex of the feasible region also find the values of x and y for which the objective function z = ax + by has maximum or minimum value (as the case may be).

Solve the following linear program

maximise 5x_{1}+ 6x_{2}

subject to

x_{1}+ x_{2}

x_{1}- x_{2}>= 3

5x_{1}+ 4x_{2}

x_{1}>= 0

x_{2}>= 0**Step 1 :**It is plain that the maximum occurs at the intersection of

5x_{1}+ 4x_{2}= 35 and

x_{1}- x_{2}= 3**Step 2 :**Solving simultaneously, rather than by reading values off the graph, we have that

5(3 + x_{2}) + 4x_{2}= 35

i.e. 15 + 9x_{2}= 35**Step 3 :**i.e. x

_{2}= (20/9) = 2.222 and

x_{1}= 3 + x_{2}= (47/9) = 5.222

The maximum value is 5(47/9) + 6(20/9) = (355/9) = 39.444**Answer :**39.444

A carpenter makes tables and chairs. Each table can be sold for a profit of £30 and each chair for a profit of £10. The carpenter can afford to spend up to 40 hours per week working and takes six hours to make a table and three hours to make a chair. Customer demand requires that he makes at least three times as many chairs as tables. Tables take up four times as much storage space as chairs and there is room for at most four tables each week.

Formulate this problem as a linear programming problem .**Step 1 :**Variables

Let

x_{T}= number of tables made per week

x_{C}= number of chairs made per week**Step 2 :**Constraints

total work time

6xT + 3xC

customer demand

xC >= 3xT

storage space

(xC/4) + xT

all variables >= 0**Step 3 :**Objective

maximise 30x_{T}+ 10x_{C}

The graphical representation of the problem is given below and from that we have that the solution lies at the intersection of

(x_{C}/4) + x_{T}= 4 and 6x_{T}+ 3x_{C}= 40

Solving these two equations simultaneously we get x_{C}= 10.667, x_{T}= 1.333 and the profit = £146.667**Answer :**x

_{C}= 10.667, x_{T}= 1.333 and the profit = £146.667