7.3. Graphical Representation

Try these first

1. 1.

   What is the objective function in the sweets shop example?

   Hint

   Think about how much profit each sweet generates.

2. 2.

   Define feasible region in the context of linear programming.

   Hint

   Where do all the constraints overlap?

3. 3.

   What is the primary goal of linear programming?

   • To minimize variables
   • To maximize or minimize an objective function
   • To graph equations

   Hint

   Consider what we want to achieve in optimization.

4. 4.

   True or False: The Simplex Algorithm guarantees finding the optimal solution at non-vertex points.

   • True
   • False

   Hint

   Look at where the constraints intersect.

5. 5.

   Given the constraints of a sweets shop 'b ≤ 200', 'h ≤ 300', and 'b + h ≤ 400', graph the feasible region and explain its shape.

   Hint

   Plot each line carefully and identify intersections to visualize your region.

6. 6.

   If you add a new product, say almond rasmalai, with a profit of 1300 per box and only limited by milk constraints, how would you redefine your problem in terms of variables and constraints?

   Hint

   Consider how much milk each type of sweet needs when formulating your new limits.