linear programming- shadow prices

ToyWorld makes soldiers (:31), trains (x2) and dolls (x3) and the LP for maximizing ToyWorld's monthly prot (in dollars) is as follows. max 3 = $20331 + $43332 + $43333 s.t. 21:1 | 4332 + 5x3 3 250 (Hours) Prot Objective Function) Carpentry Constraint) 3x1 + 71E2 + 5x3 3 320 (Hours) 331,332,133 2 0 Painting Constraint) Sign Restrictions) ( ( 331 + 2x2 + 3x3 3 140 (Hours) (Sanding Constraint) ( ( We are given that the optimal solution results in ToyWorld making some of all three types of toys: soldiers, trains and dolls. a.) (5 points) Using only matrix algebra (no simplex method) determine the optimal tableau, and from this determine how many of each (soldiers, trains and dolls) should be made and ToyWorld's monthly prot. b.) (5 points) Determine the shadow prices for each of the three constraints 0.) (5 points) ToyWorld wants to consider also making cars (x4), and has determined that each car requires 3 carpentry hours, 2 sanding hours and 3 painting hours. Determine how much prot must be made per car for it to become worthwhile to make any cars. d.) (5 points) Set the prot per car equal to that determined in part (c) plus one dollar and then determine which of the soldiers, trains or dolls will no longer be protable to make