4. (17 marks) An oil refinery produces two types of liquid fuels (A and B) by blending crude oils of two different grades (I and II) and certain additives (III). A and B are sold at $12 and $14 per gallon respectively. The costs of I, II and III are $7, $6 and $8.2 per gallon respectively. The table below shows availabilities of raw materials and various specifications. C There are 7,000 gallons of I available. C There are 10,000 gallons of II available. C3 There are 4,500 gallons of III available. C4 At most 35% of A is I. Cs At least 40% of A is II. C At most 10% of A is III. C At least 25% of B is I. CBI in B is no more than II in B. C. At most 30% of B is III. C10 A is at least 7,000 gallons due to a special demand The objective is to maximize the total profit. Let x, denote the number of gallons of raw material (j =I, II or III) used in the production of fuel (i =A or B). (a) Find the objective function. Express your answer in Excel-ready form. (b) Write mathematical descriptions for constraints C, C, and C- Express your answers within Excel-ready form. (c) Below is the sensitivity report generated with Excel with some terms omitted. Variable Cells Final Cell Name Value Reduced Objective Cost Coefficient Allowable Increase Allowable Decrease $C$19 k 0 0 $D$19 xAll 4925 0 5.714285714 $E$19 xAll 150 0 08.285714286 $F$19 xBI 5075 0 0 0 $G$19 xBII k 0 0 5.714285714 $H$19 xBIII 4350 0 1E+30