(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)

UESTION 1: Linear Pro rammin and Sensitivi Hanna Joy LTD. produces four products: W, X, Y and 2, 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 U3 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 Revenue per unit I Resources Cost per unit W $82 Wood meters $3 X $65 Metal (meters) $5 Y $ 1 31 Labour (hours) $4 Z $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 subjectto: 3W+10X+ 2Y+ SZ 5 2900 4W+ X+12Y+ 225 400 2W+ X+ 3Y+ Z: 300 W+ X 2 205 = 0 W,X,Yand22 0 The SOLVER solution is shown below. Z 0.00 286.05 2.33 6.98 45 26 53 34 Wood (meters) Metal (meters) Labour (hours) First two products Y and Z requirement Instructions for parts (a) to (c) below: In these three parts, the problem above is altered by adding additional features to the problem description. In each part, you are to provide a correct linear programming formulation of the new problem. You do not necessarily have to rewrite the whole formulation, as long as you can clearly and unambiguously indicate what should be done. The three parts are independent of each other (i.e. when doing one of the parts, ignore all of the others)