Reference no: EM133129823
Newfort Glass Company (NGC) has two plants in North Texas that make insulated glass (IG) products and tempered glass (TG) products for commercial and residential use in the region. Each week, NGC needs to decide how to allocate the production of orders across the two plants. Both insulated glass and tempered glass production involve three main steps: cutting, edging (also called seaming or polishing), and finally tempering, which involves heat-treating the glass in a furnace. These three steps are performed at stations (or "cells") that operate independently inside each plant (i.e., they are not part of a continuous production line). The two plants utilize different technologies and so they perform the three main steps at different rates, measured in SQFT of finished product per hour.
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PLANT 1
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IG 1
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TG 1
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PLANT 2
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IG 2
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TG 2
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Cutting 1
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500 SQFT/HR
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500 SQFT/HR
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Cutting 2
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700 SQFT/HR
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700 SQFT/HR
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Edging 1
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400 SQFT/HR
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250 SQFT/HR
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Edging 2
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500 SQFT/HR
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400 SQFT/HR
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Furnace 1
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400 SQFT/HR
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600 SQFT/HR
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Furnace 2
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600 SQFT/HR
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800 SQFT/HR
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The variable costs (labor, materials, energy, etc.) associated with production at each plant are different as well (measured in $/SQFT):
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PLANT 1
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IG 1
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TG 1
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PLANT 2
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IG 2
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TG 2
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$9 per SQFT
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$7 per SQFT
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$8 per SQFT
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$6 per SQFT
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NGC employs two 8-hr shifts per day and operates 5 days per week at each plant. Total orders for finished product this week are for 38000 SQFT of insulated glass and 23000 SQFT of tempered glass. How should NGC allocate their glass production across the two plants this week?
A. Write down the LP formulation for NGC's production problem.
B. Solve your model in Excel. Indicate your optimal solution (i.e., production schedule) and optimal value (i.e., minimum cost).
C. Would improving the efficiency of the furnace at either plant help reduce costs? Why or why not? What operation(s) at what plants are most critical to the production of glass?