# A merchant plans

Let x be the units be desktop demanded, and y be the units of

Portable model demanded.

According to a question we have the following objective function

and constraints.

Here the objective is to maximise profit.

Objective function: z = 4500x + 2500y

Constraint:

x + y ≤ 250

25000x + 40000y ≤ 70,00,000

5x + 8y ≤ 1400

x ≥ 0, y ≥ 0

The maximum value of z can only be obtained at the corner points of the feasible region. So we need to check the value of z at all corner points of the feasible region.

So, first, we will be finding out the feasible region by drawing the regions defined by constraints.

For plotting feasible region, we will be using the fundamentals of a straight line to get the feasible region as shown in the figure.

Clearly ABCD represents the feasible region and corner points are determined by solving:

x + y = 250 and 5x + 8y = 1400

x = 0 and 5x+8y = 1400

y = 0 and x + y = 250

& x = 0 and y = 0

To solve -

Value of objective function z

at point A = 4500(250) + 2500(0) = 1125000

Value of Z at point B = 4500×(200) + 2500(50) = 1150000

Value of Z at point C = 4500(0) + 2500(175) = 875000

Value of Z at point D = 4500×0 + 2500× 0 = 0

Z is maximum at point C (200,50)

Profit will be maximised for 200 units of x and 50 units of y and the maximum value of Z = maximum profit = Rs. 1150000

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses
RELATED QUESTIONS :

Corner points of Mathematics - Exemplar

Using the method Mathematics - Board Papers

Refer to ExerciseMathematics - Exemplar

A dietician wisheRD Sharma - Volume 2

A merchant plans Mathematics - Board Papers

A dietician wisheMathematics - Board Papers

Maximise and MiniMathematics - Exemplar