Metal Fabricators, Inc. manufacturers gas grill tanks, Model # 1420, for four original equipment manufacturers (OEMs). Demand is forecast to be as follows: Quarter 1 2,900 tanks, Quarter 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 vary as follows: Quarter 1 $24.70 per tank, Quarter 2 $29.40, Quarter 3 $27.20, and Quarter 4 $30.50. Due to production contracts with the OEMs, no shortages are allowed. Beginning inventory for Quarter 1 is 320 tanks. At the end of each quarter, inventory holding costs are $4.50 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:
	Pi = number of units produced in month i,
	Ii = inventory at the end of month i

Minimal total cost

=

P1

+

P2

+

P3

+

P4

+

I1

+

I2

+

I3

The constraints are as follows:

Week 1: P1	+		+	I1	-Select-=Item 11
Week 2: I1	+	P2	+	I2	-Select-=Item 16
Week 3: I2	+	P3	+	I3	-Select-=Item 21
Week 4: I3	+	P4	+	I4	-Select-=Item 26
Pt, It 0 for t = 1, 2, 3