E&E Refinery produces 3 types of gasoline: standard, midgrade, and premium by distilling from crude oil. Distilling 1 liter of crude oil can generate 0.5 liter of standard gasoline and 0.3 liter of midgrade gasoline. One liter of standard gasoline can be further processed into 1 liter of premium gasoline. The distillation of 1 liter of crude oil requires 1 machine hour and the cost of purchasing 1 liter of crude oil is 2 dollars ($2). It takes 3 additional machine hours and $2 to process 1 liter of standard gasoline into 1 liter of premium gasoline. Standard gasoline can be sold at the price of $4 per liter and midgrade gasoline can be sold at the price of $6 per liter. The price for premium gasoline is $10 per liter.

Each week, E&E Refinery has 4,000 machine hours available and can purchase up to 3,000 liter of crude oil. The goal is to maximize the weekly profit.

a) Formulate a math model for the problem using the following decision variables defined:

XCdenote the number of liters of crude oil used per week,

XSdenote the number of liters of standard gasoline produced per week after deducting the amount used to produce premium gasoline,

XMdenote the number of liters of midgrade gasoline produced per week, and

XPdenote the number of liters of premium gasoline produced per week

b)Use Excel solver to obtain the optimal solution for this problem and the maximum profit.

XC =?.

XS =?.

XM =?.

XP =?

c)The company has two options for procuring extra resources. Option 1 is to buy at least 1,500 liters of crude oil at $500 from another supplier. Option 2 is to rent a new machine which will provide additional 3,500 machine hours at a weekly cost of $4,500. Which option is better for the company? Please explain your reasons for your option.