A retailer must decide whether to build a small or large facility at new location. Demand at the location can be either low or high, with estimated probabilities to be $0\mathrm{.}4$ and $0\mathrm{.}6,$ respectively. Plan production for a four$-$month period: February through May. For February and March, you should produce to exact demand forecast. For April and May, you should use overtime and inventory with a stable workforce; stable means that the number of workers needed for March will be held constant through May. However, government constraints put a maximum of $5000$ hours of overtime labor per month in April and May $($zero overtime in February and March$).$ If demand exceeds supply, then backorders occur. Assume zero inventory on February $1.$ There are $100$ workers on January $31.$ You are given the following demand forecast: February $80000$; March, $64000$; April, $100000$; May, $40000.$ The other relevant information is given below: