Part 2 [30 points] The Vallejo renery can produce four types of oil products: Premium Gasoline (P), Regular Gasoline (R), Diesel (D) and Motor Oil (M) and the gross margins! gallon for these products are: P $22, R $16, D $11 and M $18. Four inputs are used in the production Crude Oil, Plant, Labour and Energy. The maximum weekly quantities available of these inputs are 600,150,140 and 130 respectively. The blending proportions are: Premium Regular Diesel Motor Oil (P) R) (D) (M) Crude 70 45 18 65 s 600 Plant 10 15 22 34 S 150 Labour 12 20 8 30 S 140 Energy 1 5 8 10 5 S 130 The attached answer and sensitivity reports maximises the gross margins to the renery. Use the attached printouts to answer the following questions. (a) How much of each oil products that the renery should produce? (b) If the renery marketing manager insisted on producing a full range of oil products, would this affect the total gross margin? If so, explain how much would it cost per unit produced. (c) If the labour union argued that the productivity of their members justied a wage increase of $5.50 per hour, explain whether you would agree or disagree. ((1) How much could the crude oil capacity be expanded before the types of oil products produced would change? Explain. (e) If per unit gross margin for premium gasoline (P) decreases to $20, would this cause changes in the optimal production quantities? How about the value of the objective function? Explain. (f) What are the slacks on the crude oil, plant and labour constraints? Is there any relationship between slacks and shadow prices? Explain. Microsoft Excel 16.0 Answer Report Worksheet: [Vallejo Refinery.xIs]Sheet1 Report Created:25/05/2022 10:39:25 AM Objective Cell (Max) Original Cell Name Value Final Value $B$6 Objective Function Value 0 198.512 Variable Cells Original Cell Name Value Final Value Integer $B$5 Production Premium 0 6.628 Contin $C$5 Production Regular 0 2.647 Contin Production Diesel O $D$5 0.940 Contin $E$5 Production Motor Oil 0 0 Contin Constraints Cell Cell Name Value Formula Status Slack $G$10 Crude Oil 600 $G$10