7.9. Justifying Optimum Profit

Try these first

1. 1.

   Define the term 'Objective Function' in the context of linear programming.

   Hint

   Think about what you are trying to maximize or minimize.

2. 2.

   What is a feasible region?

   Hint

   Consider the graphical representation of constraints.

3. 3.

   What does the 'feasible region' represent in a linear programming problem?

   • All possible combinations of solution values
   • Only the maximum value area
   • The least profitable region

   Hint

   Consider what 'feasibility' means in this context.

4. 4.

   True or False: The optimal solution for a linear programming problem can be anywhere in the feasible region.

   • True
   • False

   Hint

   Think about the nature of linear functions.

5. 5.

   A factory produces widgets and gadgets. The profit from each widget is 150 rupees, and gadgets 400 rupees. Given the constraints on production as follows: Widgets ≤ 300, Gadgets ≤ 200, and total items ≤ 400. Compute the optimal production strategy for maximum profit.

   Hint

   Draw the constraint graph and find intersections.

6. 6.

   Imagine you want to maximize space in a circular garden by planting a combination of roses and lilies. Given specific sunlight requirements and nutrient needs, develop a linear programming model to decide the optimal number of each type of plant.

   Hint

   Relate your constraints to available area and sunlight distribution.