$1.$ Explain following terms:Production function, $[5$pts$]2.$ Marginal product, TRS$,$ Returns to scale, Isoprofit line, Isocost line.Justify whether the following statement is true or false. If the productionfunction is $2$y$==,$ then it exhibits constant returns to scale. $[5$pts$]$f$($ xx$1)2$xx$,2123.$ Justify whether the following statement is true or false. If the value of themarginal product of labor exceeds the wage rate, then a competitive, profit maximizingfirm would want to hire less labor. $[5$pts$]4.$ Justify whether the following statement is true or false. A competitive, cost$-)$f $+($ xminimizing firm has the production $2$xxx$12,2=$ and currently uses positive$1$amount of both inputs. If the price of $1$ x doubles and the price of $2$x triples, then the totalcost of production will be more than doubled. $[5$pts$]5.$ A profit$-$maximizing competitive firm uses just one input, x$,$ to produce output y$.$Its production function is $2$y$=8$x$1/.$ The price of output is $40$$ each unit and the factorprice is $8$$ each unit. Find profit$-$maximizing output and the amount of the factor that thefirm demands. Find also the maximum profits. Explain and show all working steps$[10$pts$]6.$ A firm faces production function Q$($L$,$K$)=20$LK$.[15$pts$]$a$.$ b$.$ c$.$ Write the cost minimization problem for this firm?Determine the demand curves for labor and capital $($L and K$)$ as a function of Q$,$r$,$w$.$what is the cost minimizing input combination if the firm wants to produce $1000$units per year and if w $=1$ and r $=2?$d$.$ What if the firm is restricted to $$K units of capital in the short$-$run,