Maximize Z $=12$x$1+18$x$2+15$x$3$ where x$1=$ the quantity of product $1$ to make, etc.Subject to: Machine $5$ x$1+4$ x$2+3$ x$3160$ minutesLabor $4$ x$1+10$ x$2+4$ x$3288$ hoursMaterials $2$ x $1+2$ x $2+4$ x $3200$ poundsProduct $2$ x $216$ units x $1,$ x $2,$ x $30$ Are any constraints binding? If so$,$ which one$($s$)?$If the profit on product $3$ were changed to $$22$ a unit, what would the values of the decision variables be$?$ The objective function? Explain.If the profit on product $1$ were changed to $$22$ a unit, what would the values of the decision variables be$?$ The objective function? Explain.If $10$ hours less of labor time were available, what would the values of the decision variables be$?$ The objective function? Explain.If the manager decided that as many as $20$ units of product $2$ could be produced $($instead of $16),$ how much additional profit would be generated?If profit per unit on each product increased by $$1,$ would the optimal values of the decision variables change? Explain. What would the optimal value of the objective function be$?$ Consider this situation: A manager is contemplating making changes to a single$-$server system that is expected to double the service rate, and still have just one server. a$.$ Would you $($intuitively$)$ think that doubling the service rate of a single$-$server system would cut the average waiting time in line in half?b$.$ For the sake of analysis, suppose the current system has an arrival rate of $8$ customers per hour and a service rate of $10$ customers per hour. If the service rate is doubled, what impact will that have on the average number waiting in line?c$.$ What are some managerial implications of your analysis?