7.2. Formulating the Linear Program

Try these first

1. 1.

   Define linear programming.

   Hint

   Think about optimization in math.

2. 2.

   What does the objective function represent?

   Hint

   Related to profit in our sweets shop example.

3. 3.

   What does linear programming aim to do?

   • Minimize costs
   • Maximize outputs
   • Both

   Hint

   Think about both contexts in which LP can be applied.

4. 4.

   Is the profit function of the sweets shop linear?

   • True
   • False

   Hint

   Consider the nature of the profit formula.

5. 5.

   Consider a different sweets shop that produces barfis (100 rupees), halwas (600 rupees), and rasmalais (1300 rupees). The shop can't produce over 600 sweets in total and the demand is up to 300 for halwas and 200 for barfis. Formulate the LP and solve for maximum profit.

   Hint

   Draw out the constraints to visualize the feasible region.

6. 6.

   If a new constraint was added where rasmalai requires three times the milk as halwa, how would that change the feasibility?

   Hint

   Sketch this new line against your original constraints.