Correct your numerical answers to 4 DECIMAL PLACES when necessary.

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(c) Below is the sensitivity report generated with Excel with some numbers omitted. Variable Cells Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $B$19 xA1 500 0 0 1E+30 $C$19 xA2 1200 un 0 $D$19 xA3 1200 O 5 0 SE$19 xB1 5900 O 1E+30 0 $F$19 xB2 8800 0 0 3.5 $G$19 xB3 6300 0 0 3.5 $H$19 xC1 1500 0 3.5 1E+30 $1$19 xC2 0 -3.5 3.5 1E+30 $J$19 xC3 0 -3.5 3.5 1E+30 Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $B$23 K1 m1 8 8000 2230.769231 5900 $B$24 K2 7 10000 1E+30 3571.428571 $B$25 K3 4 7500 8333.333333 4142.857143 $B$26 K4 -300 m2 0 1E+30 300 $B$27 K5 0 0 0 300 1200 $B$28 K6 0 0 0 600 1200 $B$29 K7 -1450 0 0 1E+30 1450 $B$30 K8 -2500 O 1E+30 2500 0 0 $B$31 K9 0 0 1E+30 0 $B$32 K10 -1500 3.5 1500 5900 $B$33 K11 -3000 N 3000 9666.666667 $B$34 K12 -21000 0 -2000 1E+30 19000 (i) Find the values of m, and m2. Justify your answers. ) At optimal solution, what is the proportion of iron, copper and aluminum in alloy B? (iii) If the selling price of alloy C is increased by $1, how would the optimal solution be affected? Justify your answer. (iv) If the supplies of raw metals are each decreased by 1000 kg, how would the maximum total profit change? Justify your answer.2. (18 marks) A company produces three kinds of alloys (A, B and C) from three kinds of raw metals - iron (1), copper (2) and aluminum (3). The alloys are then sold to various manufacturers for further processing and productions. The amounts of the raw metals available for purchase from a provider and various specifications on the products are listed below. K1 There are 8000 kg of iron available. K2 There are 10000 kg of copper available. K3 There are 7500 kg of aluminum available. K4 At least half of A is iron. K5 No more than 40% of A is copper. K6 No more than 40% of A is aluminum. K7 No more than 35% of B is iron. K8 At least 30% of B is copper. K9 The aluminum in C is no more than the copper in C K10 There is at least 1500 kg of iron in C. K11 At least 3000 kg of A should be produced due to special demands. K12 At least 2000 kg of B should be produced due to special demands. Management of the company has decided that the alloys A, B and C will be sold at $10, $12 and $8.5 per kilogram respectively. The raw metal provider charges $4, $5 and $8 for each kilogram of iron, copper and aluminum respectively. The objective is to maximize total profit. To set up a linear program for the problem, define the variables xij = total amount of raw metal / used in the production of alloy where i = A, B or C, and / = 1 (iron), 2 (copper) or 3 (aluminum) (a) Find the objective function. Put it in Excel-ready form. (b) Find mathematical descriptions for constraints KI to K12. Put them in Excel-ready form with the inequality sign S