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

Question $2$

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letal Fabricators, Inc. manufactures gas grill tanks, Model # $1420,$ for four original equipment manufacturers $($OEMs$).$ Demand is forecast to be as follows: Quarter $1-2,900$ tanks, Uuarter $2-3,600,$ Quarter $3-3,800,$ and Quarter $4-3,000.$ Due to a hedging program for sheet steel and increases in international tariffs, production cost per quarter varies as fol Quarter $1-$ $$24\mathrm{.}70$ per tank, Quarter $2-$ $$29\mathrm{.}40,$ Quarter $3-$ $$27\mathrm{.}20,$ and Quarter $4-$$$30\mathrm{.}50.$ Due to production contracts with the OEMs, no shortages are allowed. Beginning inver or Quarter $1$ is $320$ tanks. At the end of each quarter, inventory holding costs are $$4\mathrm{.}50$ per tank. Formulate this as a linear optimization model but do not solve. Round your answers he 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 bla if the constant is one or minus one, enter $"1"$ or $"-1"$ correspondingly.

Let:

$P_i=$ number of units produced in month $i,$

$I_i=$ inventory at the end of month $i$

The constraints are astrollows:

Week $1$: $P_1+P_2{P}_3$

P$4$

$I_1$

$$

$$

$I_1$

Week $2$: ${}_{I_1}+P_2+8I_2$

Week $3$: $I_2+P_3+I_3$

$3_{I_3}+P_4+$

Week $4$: $$ I$4P_t,I_{t}0$ for $t=1,2,3$

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