Question 2 ts-Dilla Joints ( × kboard/execute/content/file?cmd-view&content; id-

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Question 2

ts-Dilla Joints ( × kboard/execute/content/file?cmd-view&content; id- 2175274 1&course; id-_97647.1 of profits, respectively. Those furnitures require 10, 20, and 30 sq. feet of woods respectively, and 5, 10, and 20 sq. ft of fabrics, respectively. Also they require 2, 3 and 5 hours of labor, respectively. If 2000 sq.ft of woods, 1000 sq. ft of fabric and 400 hours of labors are available, how many chairs, desks and tables should be made to maximize the profit? Formulate. (10) 2. Rod Ent packages and ships cheese trays to four different retailers. He has operations on both the East and West Coasts and in the Midwest. The cost of packaging is $3.10 per tray on the West Coast, $3.25 per tray on the East Coast, and $3.15 per tray in the Midwest. Rod's forecasts for demand indicate that shipments must be as indicated in Table (a). Packaging capacity on the west Coast is 8000 trays, on the East Coast 7000 trays, and 10, 000 trays in the Midwest. The shipping costs from the three locations to the four retailers are given in Table (b). Formulate this LP problem. Table (a) Retailer Demand Retailer Demand 4 7,000 5,000 ,000 6,000 Table (b) Shipping Costs per Tray To Retailer From Location West Coast Midwest East Coast 0.02 0.03 0.04 2 0.03 0.02 0.04 3 0.02 0.04 0.03 4 0.05 0.03 0.04 (10) 3. Solve the following LP model graphically maximize z= 8x1 + 2x2 subject to 2x, +4x, 22 -x1 + 4x2£10

Explanation / Answer

(2) Formulate LP problem

Decision variables: Xij = Quantity packaged and shipped from location i to Retailer j , where i {1,2,3} for the three locations - West Coast, Midwest, East Coast and j {1,2,3,4} for the four retailers

Objective: Min 0.02X11 + 0.03X12 + 0.02X13 + 0.05X14 + 0.03X21 + 0.02X22 +0.04X23 + 0.03X34 + 0.04X31 + 0.04X32 + 0.03X33 + 0.04X34 + 3.1*(X11+X12+X13+X14) + 3.25*(X21+X22+X23+X24) + 3.15*(X31+X32+X33+X34)

s.t.

X11+X12+X13+X14 <= 8000

X21+X22+X23X+X24 <= 7000

X31+X32+X33+X34 <= 10000

X11+X21+X32 = 5000

X12+X22+X32 = 7000

X13+X23+X33 = 6000

X14+X24+X34 = 7000

X11, X12, X13, X14, X21, X22, X23, X24, X31, X32, X33, X34 >= 0

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