MOD B: LINEAR PROGRAMMING Step $1$: Enter the LP model: Leach Distributors packages and distributes industrial supplies. A standard shipment can be packaged in a class A container, a class K container, or a class T container. A single class A container yields a profit of $$9$; a class K container, a profit of $$7$; and a class T container, a profit of $$15.$ Each shipment prepared requires a certain amount of packing material and a certain amount of time. Leach distributors is commited, based on customer demand, to inventory at least $11$ A containers. $$ Class A Class K Class T x$4$ x$5$ RHS Objective Function $$9$ $$7$ $$15$ Packing Material $2\mathrm{.}001\mathrm{.}003130<=$ Packing Time $2\mathrm{.}006\mathrm{.}004240<=$ A$111>=$ Constraint $4$ RESOURCES NEEDED PER STANDARD SHIPMENT Constraint $5$ Class of Container Packing Material $($Pounds$)$ Packing Time $($Hours$)$ Constraint $6$ A $22$ Constraint $7$swaqqq K $16$ Constraint $8$ T $34$ Constraint $9$ Total Resources Available Each Week $130240$ Constraint $10$ Formulate and solve this problem using LP software. Step $2$: Calculate the LHS in Constraints $$ LHS RHS a$.$ What is the product mix A $=[$Blank$1],$ K $=[$Blank$2],$ T $=[$Blank$3]$ Constraint $121300130130$ Constraint $226400240240$ A $11$ round to the nearest whole number Constraint $3100001111$ Constraint $40000000$ K $16$ round to the nearest whole number Constraint $50000000$ Constraint $60000000$ T $31$ round to the nearest whole number Constraint $70000000$ Constraint $80000000$ b$.$ What is the total profit? $$[$Blank$4]$ Constraint $90000000$ Constraint $100000000$$$670\mathrm{.}71$ Step $3$: Run the Solver from the 'Data' tab in the Top Ribbon c$.$ Are there any unused resources? $[$Blank$5]$ If so$,$ which constraint and by how much? $[$Blank$6]$ Optimal Solution x$1$ x$2$ x$3$ x$4$ x$5$ Profit $1115\mathrm{.}85730\mathrm{.}71400$ $$670\mathrm{.}71$ Unused Resources? No

Amount: All resources are utilized d$.$ What if packing material was reduced by $10$ pounds. how would that impact profits? $[$Blank$7]$ Profits would be reduced by $$44\mathrm{.}29$ e$.$ Given the reduction that took place in letter d$.,$ what would be the new resource allocation? $[$Blank$8]$ A $-11,$ K $-19,$ T $-27$