Your company produces three grades of gasolines for industrial distribution. The three gradespremium, regular and economy-are produced by refining a blend of three types of crude oil: Brent, Dubai and WTI. Each crude oil differs not only in cost per barrel, but in its composition as well. Table 1 below indicates the percentage of three crucial compounds found in each of the crude oils, the cost per barrel for each, and the maximum weekly availability of each.

Table 1: Ingredient Data

Crude Oil Type	Compound A (%)	Compound B (%)	Compound C (%)	Cost/Barrel ($)	Availability (barrels)
Brent	35	25	35	86	15,000
Dubai	50	30	15	92	32,000
WTI	60	20	15	95	24,000

Table 2 indicates the weekly demand for each grade of gasoline and the specific conditions on the amounts of the different compounds that each grade of gasoline should contain. The table shows, for example, that in order for gasoline to be classified as premium grade, it must contain at least 55% of compound A, no more than 23% of compound B and no restrictions on compound C. Your company must decide how many barrels of each type of crude oil to buy each week for blending to satisfy demand at minimum cost.

Table 2: Gasoline Data

Gasoline Type	Compound A	Compound B	Compound C	Demand (barrels)
Premium	55%	23%		14,000
Regular		25%	35%	22,000
Economy	40%		25%	25,000

1. Write down the linear program to determine the optimal blending plan. (8 marks)

2. Set up the Excel spreadsheet and use Solver to compute the optimal plan. Interpret your Solvers answer report. (8 marks)

3. Your company finds a new crude oil supplier who can sell you unlimited Brent oil at current cost.

a. Which constraint(s) should you remove from your LP in Q1? (2 marks)

b. Set up the corresponding LP in Excel and run Solver. (2 marks)