Problem 2) a Set up variables Xnb of tons cuf compond X yo no of tons of compoundy. b) Graphically У (0,20) _x(+) y (x)=1 - 1/3 · (x (+)+ 1 (+10)=2) y (t)-y (30) = 1-33 y () = 3 y= 20 x 12 ( 1-3 (t)= Set up constraints 48 x (4) + y ( ) ≥ 4 (0,12) B% x (+) + y (to) 22 x (1/2) + y (12) 21 (0,8) х, ухо Set up optimal equation Min Z=250&x + 200$y Z S 4 z= 8000 3 (80) (120) (x,y) = ( 12, 20) ✗ (16,0) Problem 2 A firm produces three types of refined chemicals: A, B, and C. At least 4 tons of A, 2 tons of B, and 1 ton of C have to be produced per day. The inputs used are compounds X ton of C. Each ton of Y and Y. Each ton of X yieldston of A, ½ ton of B, and yields ½½ ton of A, 4 12 12 ton of B, and ½ ton of C. Compound X costs $250 per ton, compound Y $400 per ton. The cost of processing is $250 per ton of X and $200 per ton of Y. Amounts produced in excess of the daily requirements have no value, as the products undergo chemical changes if not used immediately. The problem is to find the mix with minimum cost input. a) Formulate this problem as a linear programming problem with the objective of minimizing total daily costs. b) Find the optimal solution graphically. c) The daily requirement for C is increased to 1.25 tons. By how much does the daily cost increase? The daily requirement for B is increased to 2.25 tons. By how much does the daily cost increase? The daily requirement for A is reduced by 0.5 ton. By how much does the daily cost change? d) Determine for each individual compound the range of prices for which the present solution remains optimal. e) The firm receives an offer for a third compound that yields ½-½ ton of A, ½ ton of B, 1 and ton of C at a price of $300 per ton and a processing cost of $300 per ton. 10 Should the firm accept this offer? Why or why not?

Problem 2) a Set up variables Xnb of tons cuf compond X yo no of tons of compoundy. b) Graphically У (0,20) _x(+) y (x)=1 - 1/3 · (x (+)+ 1 (+10)=2) y (t)-y (30) = 1-33 y () = 3 y= 20 x 12 ( 1-3 (t)= Set up constraints 48 x (4) + y ( ) ≥ 4 (0,12) B% x (+) + y (to) 22 x (1/2) + y (12) 21 (0,8) х, ухо Set up optimal equation Min Z=250&x + 200$y Z S 4 z= 8000 3 (80) (120) (x,y) = ( 12, 20) ✗ (16,0) Problem 2 A firm produces three types of refined chemicals: A, B, and C. At least 4 tons of A, 2 tons of B, and 1 ton of C have to be produced per day. The inputs used are compounds X ton of C. Each ton of Y and Y. Each ton of X yieldston of A, ½ ton of B, and yields ½½ ton of A, 4 12 12 ton of B, and ½ ton of C. Compound X costs $250 per ton, compound Y $400 per ton. The cost of processing is $250 per ton of X and $200 per ton of Y. Amounts produced in excess of the daily requirements have no value, as the products undergo chemical changes if not used immediately. The problem is to find the mix with minimum cost input. a) Formulate this problem as a linear programming problem with the objective of minimizing total daily costs. b) Find the optimal solution graphically. c) The daily requirement for C is increased to 1.25 tons. By how much does the daily cost increase? The daily requirement for B is increased to 2.25 tons. By how much does the daily cost increase? The daily requirement for A is reduced by 0.5 ton. By how much does the daily cost change? d) Determine for each individual compound the range of prices for which the present solution remains optimal. e) The firm receives an offer for a third compound that yields ½-½ ton of A, ½ ton of B, 1 and ton of C at a price of $300 per ton and a processing cost of $300 per ton. 10 Should the firm accept this offer? Why or why not?