Problem $14-28$ Algo $($Using Optimization Models for Resource Management$)$

Question $2$ of $6$

Hint$($s$)$ Check My Work

Metal Fabricators, Inc. manufactures gas grill tanks, Model # $1420,$ for four original equipment manufacturers $($OEMs$).$ Demand is forecast to be as follows: Quarter $1-3,400$ tanks, Quarter $2-4,100,$ Quarter $3-4,300,$ and Quarter $4-3,500.$ Due to a hedging program for sheet steel and increases in international tariffs, production cost per quarter varies as follows: Quarter $1-$$$28\mathrm{.}20$ per tank, Quarter $2-$$$33\mathrm{.}60,$ Quarter $3-$$$31\mathrm{.}10,$ and Quarter $4-$$$34\mathrm{.}80.$ Due to production contracts with the OEMs, no shortages are allowed. Beginning inventory for Quarter $1$ is $380$ tanks. At the end of each quarter, inventory holding costs are $$5\mathrm{.}10$ per tank. Formulate this as a linear optimization model but do not solve. Round your answers for the coefficients for objective function to two decimal places and round other answers to the nearest whole number. Use a minus sign where appropriate and do not leave any fields blank. If the constant is one or minus one, enter $"1"$ or $"-1"$ correspondingly.

Let: