Indicate graphically whether the following linear program has a feasible solution.Maximize Z $=$ x$1+2$x$2,$subject to: x$1-2$x$2=3,$ x$1+\backslash$times $23,$X$10,$x$2=0.$

A fertilizer company purchases nitrates, phosphates, potash, and an inert chalk base at a cost of $$1500,$$$500,$$$1000,$ and $$100$ per ton, respectively, and produces four fertilizers $A,B,C,$ and $D.$ The production cost, selling price, and composition of the four fertilizers are given below.

$\backslash$table$[[$Fertilizer$,$ Production

$cost$

$(\frac{\text{\$}}{t}on),$Selling price $($$$/$ton$),$Percentage composition by weight$],[$Nitrates$,$Phosphates,Potash,Inert chalk base$],[$A$,100,350,5,10,5,80],[$B$,150,550,5,15,10,70],[$C$,200,450,10,20,10,60],[$D$,250,700,15,5,15,65]]$

During any week, no more than $1000$ tons of nitrate, $2000$ tons of phosphates, and $1500$ tons of potash will be available. The company is required to supply a minimum of $5000$ tons of fertilizer A and $4000$ tons of fertilizer $D$ per week to its customers; but it is otherwise free to produce the fertilizers in any quantities it pleases. Formulate the problem of finding the quantity of each fertilizer to be produced by the company to maximize its profit.

Describe how you can proceed to find a solution to the problem formulated above.