Question

2. Geniue Antique Egyptian Artifacts, Inc. produces three varieties of antique artifacts for sale to tourists: statuettes, lamps, and urns. All of the artifacts include special tlay. A statuette requires 13 ounces of clay, a lamp uses 18 ounces, and each urn takes 17 ounces. Existing capacity of clay is 28,000 ounces per month. A special material is also used to produce the three artifacts, with each statuette needing 0.8 ounces, each lamp 0.7 ounces, and a typical urn requiring 1.0 ounces. The company has inventory of 1,200 ounces of special material per month. The owner of the company wishes to maintain a balanced marketing program, and has ordered that production of statuettes to be limited to 275. The overall per unit profit for artifacts is the following: $199 per statuette, $99 per lamp, and $145 per urn. The owner wants to know how much of each type of antique to fabricate monthly in order to optimize profit. Formulate and present a linear programming model for this problem using decision variables, objective function, and constraints. Solve the linear program developed in part (a), to determine the optimal production plan. a. b.

Answer 1

Formulation of Linear programming:

Decision Variables:

Let x,y,z be the number of quantities of statutes, lamps and urns produced.

Objective : To maximize the overall profit from the sale of the three type of artifacts

Objective function: Total Profit = Sumproduct (Profit/unit , Number of units of each artifact)

Max (Profit) = 199x +99y +145z

Subject to constraints:

13x + 18y + 17z <= 28,000

(Capacity constraint for availability of clay used for production. Maximum of 28,000 ounces of clay is available)

0.8x + 0.7y + z <= 1,200

(Inventory Holding of Special material. Maximum of 1,200 ounces of special material could be used for production)

x <= 275 (Production limit of quantities of Statutes that can be manufactured)

x,y,z >= 0 (Non-Negative Integer Constraint)

Solution:

Solver Parameters Line 1 Statutes 275 Line 2 Lamps 0 Urns Set Objective: SE571 Production Qty To: Max Min Ovalue Of: 196825 Profit Subj to Constraints 275 20235 By Changing Variable Cells: SE55:$G$5 Statue Production Clay Capacity Constraint Special Material Constraint 275 28000 1200 <= Subject to the Constraints: $D$10 <= SG$10 $D$11 <= SG$11 $D$9 <= SG$9 SE$5:SGS5 = integer SE$5:$G$5 >= 0 male contrained variabler Mos Mostis

Production Quantities:

x = 275 units

y = 0 units

z = 980 units

Profit = $ 196,825