After $20$ years of hard work, Geppetto founded Pinocchio Co$.$ The company will produce luxury

desks over the next $4$ months. Forecasted demand and production costs over this time period are:

Pinocchio Co$.$ has a monthly production capacity of $300$ desks. The company currently has $30$

desks in inventory and has enough capacity to store up to $150$ desks. The holding cost of keeping

a desk in inventory for a month is $$20.$

Formulate a Linear Programming model that minimizes the cost.