linear practie - LINEAR PROGRAMMING Some Worked Examples...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
1 LINEAR PROGRAMMING : Some Worked Examples and Exercises for Grades 11 and 12 Learners. Example : A small business enterprise makes dresses and trousers. To make a dress requires 2 1 hour of cutting and 20 minutes of stitching. To make a trousers requires 15 minutes of cutting and 2 1 hour of stitching. The profit on a dress is R40 and on a pair of trousers R50. The business operates for a maximum of 8 hours per day. Determine how many dresses and trousers should be made to maximize profit and what the maximum profit is. Solution : Step 1 : To solve the above problem we would have to translate the conditions or constraints from a verbal to a symbolic form. We first introduce our variables. Let x be the number of dresses and y the number of trousers. Step 2 : Next we express the constraints as a system of inequalities . 0 y and 0 x , x and y being whole numbers ie. y , x N 0 Cutting Time: 32 y 2x ie. 8 y 4 1 x 2 1 + + Stitching Time: 48 y 3 2x ie. 8 y 2 1 x 3 1 + + Step 3 : Graph the system of inequalities and shade in the region that satisfy the constraints. The shaded region is called the feasible region . Step 4: Write the profit in terms of the variables. P = 40x + 50y Since the objective (in this case) is to make a maximum profit, the profit equation is called the objective function . Step 5: To determine the maximum profit and the number of items that will give the maximum profit we can use one of two methods : 5.1 Substitute each of the ordered pairs of the vertices of the feasible region, excluding (0;0) , ie. (0;16) , (16;0) and (12;8) into profit equation .
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern