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A business produces three products: desks, futons, and seats. These products are processed in five departments: the saw lumber, fabric cutting, sanding, staining, and assembly departments. Desks and seats are produced from raw lumber only, and the futons require lumber and fabric. Glue and thread are plentiful and represent a relatively insignificant cost that is included in operating expense. The specific requirements for each product are as follows: RESOURCE OR ACTIVITY (QUANTITY AVAILABLE PER MONTH) REQUIRED PER Desk REQUIRED PER FUTON REQUIRED PER Seat Lumber (4,350 board feet) 10 board feet @ $10/foot 5 $100/table 7.5 board feet @ $10/foot 5 $75 4 board feet @ $10/foot 5 $40 Fabric (2,500 yards) None 10 yards @ $17.50/yard 5 $175 None Saw lumber (280 hours) 30 minutes 24 minutes 30 minutes Cut fabric (140 hours) None 24 minutes None Sand (280 hours) 30 minutes 6 minutes 30 minutes Stain (140 hours) 24 minutes 12 minutes 24 minutes Assemble (700 hours) 60 minutes 90 minutes 30 minutes The company’s direct labor expenses are $75,000 per month for the 1,540 hours of labor, at $48.70 per hour. Based on current demand, the firm can sell 300 desks, 180 futons, and 400 seats per month. Sales prices are $400 for desks, $750 for futons, and $240 for seats. Assume that labor cost is fixed and the firm does not plan to hire or fire any employees over the next month. Determine the product mix needed to maximize profit at the company. What is the most limiting resource to the company? Discuss how any potential changes you might recommend to make use of excess capacity to increase profit.

RESOURCE OR ACTIVITY (QUANTITY AVAILABLE PER MONTH) REQUIRED PER Desk REQUIRED PER Futon REQUIRED PER Seat
Lumber (4,350 board feet) 10 board feet @ $10/foot 7.5 board feet @ $10/foot 4 board feet @ $10/foot
=$100/desk = $75/futon = $40/seat
Fabric (2,500 yards) None 10 yards @ $17.50/yard None
= $175/futon
Saw lumber (280 hours) 30 minutes 24 minutes 30 minutes
Cut fabric (140 hours) None 24 minutes None
Sand (280 hours) 30 minutes 6 minutes 30 minutes
Stain (140 hours) 24 minutes 12 minutes 24 minutes
Assemble (700 hours) 60 minutes 90 minutes 30 minutes
Formulation
Let X1, X2, and X3, be the number of Desks, Futons, and Seats respectively.
Objective Function: Maximize. Z = Total Profit = (400 – 100)X1 + (750 – 75 – 175)X2 + (240 – 40)X3 – 75000
or, Z = 300X1 + 500X2 + 200X3 – 75000
Subject to,
10X1 + 7.5X2 + 4.0X3 = 0
LINDO Code
Max Profit)300X1 + 500X2 + 200X3
ST
lumber) 10X1 + 7.5X2 + 4.0X3
 
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