Please solve with solver. Show and explain all work. Hint: The optimal solution to the problem is $78,450.$

Sailco Corporation must determine how many sailboats should be produced during each

of the next four quarters $($one quarter $=$ three months$).$ The demand during each of the

next four quarters is as follows: first quarter, $40$ sailboats; second quarter, $60$ sailboats;

third quarter, $75$ sailboats; fourth quarter, $25$ sailboats. Sailco must meet demands on

time. At the beginning of the first quarter, Sailco has an inventory of $10$ sailboats. At the

beginning of each quarter, Sailco must decide how many sailboats should be produced

during that quarter. For simplicity, we assume that sailboats manufactured during a quar$-$

ter can be used to meet demand for that quarter. During cach quarter, Sailco can produce

up to $40$ sailboats with regular$-$time labor at a total cost of $$400$ per sailboat. By having

employees work overtime during a quarter, Sailco can produce additional sailboats with

overtime labor at a total cost of $$450$ per sailboat.

At the end of each quarter $($after production has occurred and the current quarter's de$-$

mand has been satisfied$),$ a carrying or holding cost of $$20$ per sailboat is incurred. Use

linear programming to determine a production schedule to minimize the sum of produc$-$

tion and inventory costs during the next four quarters.