Formulate a linear programming problem

An oil company produces 2 grades of gasoline; R (regular) and E (economy) by mixing oils I and II. The table provides information regarding the oils. Note that all barrels contain 200 litres.

Answer the following questions separately to formulate a linear programming problem. At no instance should you go back to previous questions (except for the costs given in 1.1 ). Use only the current provided information and what is given at each question.

1.1) Given that a barrel of R sells for R100 and a barrel E sells for R150, write out the objective function to maximise the profit.

1.2)The maximum budget is R10 000 000.

1.3) Nor barrels R nor barrels E may comprise more than 90% of the total produced barrels.

1.4) For barrel E ingredient A must be between 40% and 50%, but taking into consideration that ingredient B may not be more than 46%.

1.5) If more than 20 000 barrels of E are sold the market starts to get saturated. There is a logarithmic decrease in the price, but for practicality you decided to model it linearly. Every barrel above 20 000 of E can only be sold for R135 and every barrel above 30 000 of E can only be sold for R130. Rewrite the objective function with additional constraints (if relevant).

1.6) A clerk was at error, a barrel of Oil II is not the standard 200 liter barrel, but 130 liter. Rewrite the objective function by taking this information into account.

Oil Ingredient A% Ingredient B% Cost/barrel 35 55 30.00 II 60 25 34.80