Question $8(20$ points$)$The saying might be My body is a temple but I see it more as acalorie$-$burning machine with flexible capacity. At this day in age,there is really not a lot of uncertainty on whether or not I am goingto be able to find my next meal. So$,$ maybe I should no longerbe applying those generous safety stock policies hunters might haveapplied ages ago, back when they might go a week without eating.In fact, after watching the P$90$X$$ infomercial, I am now thinking ofrunning my machine in a much leaner process. I have got to get ridof that excess inventory!Right now, my body weight or inventory is $190$ pounds. I estimate that my machine willburn $2,600$ calories per day on average without any exercise $($assume this holds regardlessof my weight$).$ My goal is to use P$90$X for $90$ days hoping to reduce my inventory by $10$pounds to $180$ pounds, which will hopefully be a higher percentage of muscle. The objectiveis to burn the fat off which is roughly $3,500$ calories per pound of fat. The makers of P$90$Xestimate that my machine will burn $600$ calories for each hour of P$90$X training. In otherwords, if I do a $1-$hour session each day, then I would have increased the capacity of mymachine to $3,200$ calories per day, which is to say it is indeed flexible capacity and dependson something I can control.Im not much of a dieter so the goal is to achieve the desired reduction in inventory pri$-$marily by changing the capacity of my machine through exercise; my eating, for the mostpart, will be the same. However, to ensure that I feed my machine enough protein to buildmuscle, I plan to order MET$-$Rx$$ RTD protein shakes. I can get them from The VitaminShoppe$$ online for $$37$ per case of $12$ drinks. The total cost of shipping, for any size order,is $$5$ per order. The cost of capital associated with having my money tied up in MET$-$Rxdrinks is $8\%$ per year $(365$ days per year$).$ I plan to drink one of these drinks each day. In$-$cluding the daily drink, I anticipate that my eating habits will yield the following input rates: