Hanna Joy LTD. produces four products: W, X, Y and Z, using three resources, namely wood, metal and labour. The first three constraints in the algebraic formulation and SOLVER output below are resource availability constraints. Hanna Joy LTD. must produce a total of at least 205 units of the first two products and proper use of his machinery requires that the amount of Y produced be at exactly 1/3 of the amount of Z produced. The tables below give the revenue per unit for the products, and the cost per unit for the resources. Product W X Y Z Revenue per unit $82 $65 $131 $63 Here is a correct algebraic formulation of the problem. Let W, X, Y and Z denote the number units of products W, X, Y and Z to produce. Maximize 45W + 26X+53Y+34Z subject to: 3W + 10X + 2Y + SZ 2900 4W+ X + 12Y+ 2Z 400 2W + X+ 3Y+ Z 300 W+ X 2 205 First two products Y and Z requirement 0 1 The SOLVER solution is shown below. W X Y 0.00 286.05 2.33 45 26 53 Wood (meters) 3 10 2 Metal (meters) 4 1 12 Labour (hours) 2 1 3 Resources Wood (meters) Metal (meters) Labour (hours) W, X, Y and Z 1 Y-0.33Z- 0 0 1 Z 6.98 34 5 2 1 0 0 0 -0.33 Cost per unit $3 $5 $4 7797.67 2900.00 327.91 300.00 286.05 0.00 x= 2900 400 300 205 0 (a) The price per meter of metal has risen to $6. (Hint: rewrite the objective function equation). (3 points) (b) A total of at most $10,000 is available for acquisition of the wood material. (Hint: add an additional constraint). (3 points) (c) Hanna Joy LTD. decided that the amount produced of product Y must constitute at least 30% of the total number of units produced. (Hint: add an additional constraint). (2 points) The following correct output for this problem in its original form is provided below as an Excel Solver output. You will need this output to answer questions (d) through (g) each part of which is to be considered independently of all others. Variable Cells Cell SCS8 W SDSS X SESS Y SFS8 Z Constraints Name Name Cell $G$10 Wood $G$11 Metal $G$12 Labour SGS13 Demand $G$14 Balance Final Value 0.00 286.05 2.33 6.98 Final Value 2900.00 327.91 300.00 286.05 0.00 Reduced Cost -6.60 0.00 0.00 0.00 Shadow Price 0.02 0.00 25.77 0.00 -24.35 Objective Coefficient 45 26 53 34 Constraint R.H. Side 2900 400 300 205 0 Allowable Increase 6.60 17.75 1.00 0.33 Allowable Increase 100.00 A 19.02 81.05 3.57 Allowable Decrease IE+30 0.17 16.71 5.57 Allowable Decrease 258.33 B 10.00 IE+30 6.67 (d) Two numbers have been removed from the resource sensitivity table by your professor (the letters A and B appear instead of the numbers). What are the correct values of A and B? Justify. (4 points) (e) In order to start producing product W (e.g. W>0), what would need to happen to the revenue per unit of W? Justify. (2 points) (1) Up to 15 additional hours (beyond the original 300 hours) of labour are available, at the same cost of $4/hour. What is the new optimal value of the objective function? Justify. (4 points) (g) If the revenue for product Y has changed from $131 to $121, do the optimal values of the decision variables change? Justify. What about the objective function? If you can determine what the new optimal value of the objective function is, then do so. (4 points)