Linear programming

No, there is no need. The total used for both petrols in 1.2g in order to produce 1g. The missing 0.2g is the amount lost. When formulating the constraints we show that the total used must be less than or equal to the amount available. So for example, the constraint for heavy crude is 0.7S + 0.5R <= 5,000 The 0.7 and the 0.5 are the amounts actually needed.

The refining process uses two types of crude oil – heavy and light. A mixture of these oils is blended into either Super or Regular petrol. In the refining process one gallon (g) of Super is made from 0.7g of heavy crude and 0.5g of light crude. One gallon of Regular is made from 0.5g of heavy crude and 0.7g of light crude oil. (There is a refining loss of 0.2g in each case.) At present, 5,000g of heavy crude and 6,000g of light crude oil are available for refining each day. Market conditions suggest that at least two?thirds of the petrol refined should be Super. The company makes contribution of $0.25 per gallon of Super and $0.10 per gallon of Regular. Required: (a) State the objective function and three constraints, one for heavy crude, one for light crude and one for market conditions. ? (b) Graph the constraints and shade the feasible region. (c) Deduce the optimal policy and the contribution generated, and comment briefly on your Please help me with the remaining options please

As I explain in my free lectures on this, you cannot be asked in the exam to draw the graph. You are expected to understand the graph, and I explain it in detail in the exam - have you watched the lectures? You presumably have an answer in the same book in which you found the question, so ask about whatever it is in the answer that you are not clear about and then I will explain.

B Chemicals refines crude oil into petrol. The refining process uses two types of crude oil – heavy and light. A mixture of these oils is blended into either Super or Regular petrol. In the refining process one gallon (g) of Super is made from 0.7g of heavy crude and 0.5g of light crude. One gallon of Regular is made from 0.5g of heavy crude and 0.7g of light crude oil. (There is a refining loss of 0.2g in each case.) At present, 5,000g of heavy crude and 6,000g of light crude oil are available for refining each day. Market conditions suggest that at least two thirds of the petrol refined should be Super. The company makes contribution of $0.25 per gallon of Super and $0.10 per gallon of Regular. Can you please explain that why the equation for the market condition is X equal to or greater than 2/3 (X+Y)?

The total petrol produced will be S + R. Market conditions suggest that at least two thirds of the petrol refined should be Super. Therefore S >= 2/3 (S + R). Rearranging this gives S >= 2R.