A tea company sells tea under a “premium label” and an “economy label”. Both are blended from three basic grades of tea: Premium = 60%A + 30%B + 10%C Economy = 20%A + 30%B + 50%C The market prices are $1000/tonne for premium and $750/tonne for economy. Due to the limited supply, the company can only purchase up to 100 tonnes of grade A at a cost of $800/tonne. The cost of grade B is $600/tonne and the cost of grade C is $400/tonne. To meet the demand, the total production of the two blends must be at least 200 tonnes. How much of each blend should they produce to maximise their profit (not gross but net re- turns)? Formulate an LP problem to determine this. Solve the LP using two phase simplex algorithm. Remember to define all the variables clearly and explain every step.
-
A tea company sells tea under a “premium label” and an “economy label”. Both are blended from three basic grades of tea:
Premium = 60%A + 30%B + 10%C Economy = 20%A + 30%B + 50%C
The market prices are $1000/tonne for premium and $750/tonne for economy. Due to the limited supply, the company can only purchase up to 100 tonnes of grade A at a cost of $800/tonne. The cost of grade B is $600/tonne and the cost of grade C is $400/tonne. To meet the demand, the total production of the two blends must be at least 200 tonnes.
How much of each blend should they produce to maximise their profit (not gross but net re- turns)? Formulate an LP problem to determine this. Solve the LP using two phase simplex algorithm.
Remember to define all the variables clearly and explain every step.
Step by step
Solved in 2 steps with 2 images
