Green Tech Solutions: Optimizing Production and Balancing Multiple ObjectivesPart $1$: Linear Programming for Optimal Product MixGreen Tech Solutions is a company that manufactures eco$-$friendly electronic devices. They want to determine the optimal production mix of their five products to maximize profit while adhering to resource constraints and meeting minimum production requirements.Products:$1.$Solar chargers $($x$1)2.$Energy$-$efficient laptops $($x$2)3.$Smart thermostats $($x$3)4.$LED light bulbs $($x$4)5.$Electric bike conversion kits $($x$5)$Objective:Maximize profitProfit per unit:Solar chargers: $$30$Energy$-$efficient laptops: $$150$Smart thermostats: $$80$LED light bulbs: $$10$Electric bike conversion kits: $$200$Constraints:$1.$Labor hours: $2$x$1+5$x$2+3$x$3+$ x$4+4$x$54002.$Raw materials $($in kg$)$: $3$x$1+10$x$2+4$x$3+$ x$4+8$x$56003.$Machine time $($in hours$)$: x$1+3$x$2+2$x$3+0\mathrm{.}5$x$4+2$x$53004.$Storage space $($in cubic meters$)$: $0\mathrm{.}5$x$1+2$x$2+$ x$3+0\mathrm{.}1$x$4+3$x$52005.$Minimum production of energy$-$efficient laptops and smart thermostats: x$2+$ x$3506.$Minimum production value: $30$x$1+150$x$2+80$x$3+10$x$4+200$x$55000$All variables $($x$1,$ x$2,$ x$3,$ x$4,$ x$5)$ must be non$-$negative integers.Tasks for Part $1$:$1.$Formulate the linear programming model$\mathrm{.}2.$Solve the problem using an appropriate method $($e$.$g$.,$ simplex algorithm or software tools$)\mathrm{.}3.$Interpret the results and provide recommendations for Green Tech Solutions.