$1.$ Metal Fabricators, Inc. manufactures gas grill tanks, Model # $1420,$ for four original equipment manufacturers $($OEMs$).$ Demand is forecast to be as follows: Quarter $1=2,700$ tanks, Quarter $2=3,400,$ Quarter $3=3,700,$ and Quarter $4=2,900.$ Due to a hedging program for sheet steel and increases in international tariffs, production cost per quarter vary as follows: Quarter $1=$ $$23\mathrm{.}50$ per tank, Quarter $2=$ $$28\mathrm{.}00,$ Quarter $3=$ $$25\mathrm{.}90,$ and Quarter $4=$ $$29\mathrm{.}00.$ Due to production contracts with the OEMs, no shortages are allowed. Beginning inventory for Quarter $1$ is $300$ tanks. At the end of each quarter, inventory holding costs are $$4\mathrm{.}25$ per tank.

a$.$ Formulate the problem as a linear programming model $($see Supplement D$).$

b$.$ Solve the model in $($a$)$ using Excel Solver.