Q$\mathrm{.}4(25$ Points$)$An electronics firm has a contract to deliver the following number of radios during the next three months;month $1,250$ radios; month $2,350$ radios; month $3,400$ radios. For each radio produced during months$1$ and $2,$ a $$12$ variable cost is incurred; for each radio produced during month $3,$ a $$15$ variable cost isincurred$.$ The inventory cost is $$1\mathrm{.}50$ for each radio in stock at the end of a month. The cost of setting upfor production is $$250,$ the maximum quantity to be produced is $500$ units per month, and the maximumstorage capacity is $200$ units.Radios made during a month may be used to meet demand for that month or any future month. Assumethat production during each month must be a multiple of $100.$ Given that the initial inventory level is $0$units, use dynamic programming to determine an optimal production schedule.