4. Formulate only, the following problem a) Three new products are to be produce
ID: 375611 • Letter: 4
Question
4. Formulate only, the following problem a) Three new products are to be produced b) Total production should range between 1,000 and 2,000 units. c) At least 2 items of product 1 is made for every 3 items of product 2. d) The total production of product 1 and product 2 should be half the production of product 3. e) The first 12 units of product 1 earn $17/unit, additional units vill earn $15/unit. f) Product 2 earns 10/unit. g) The first 5 units of product 3 earn $20/unit, the next 15 units earn $18/unit, the next 2,000 units earn $9/unit.Explanation / Answer
Let the three products be defined as
P1, P2, P3
P1 + P2 + P3 <= 2000
P1 + P2 + P3 >= 1000
P1/P2 >= 2/3
3P1 – 2P2 >=0
P1+P2 = 0.5*(P3)
P1 + P2 -0.5P3 = 0
Let additional variables be
P1-12 = Number of units of P1 till first 12 units
P1-12+ = Number of units of P1 more than 12 units
P1 = P1-12 + P1-12+
P3-5 = Number of units of P3 till first 5 units
P3-15 = Number of units of P3 from 6 to 15 units
P3-15+ = Number of units of P3 from 16 till next 2000 units
P3 = P3-5 + P3-15 + P3-15+
Objective function:
Maximize 17*P1-12 + 15*P1-12+ + 10*P2 + 20*P3-5 + 18*P3-15 + 9*P3-15+
Subject to:
P1 = P1-12 + P1-12+
P3 = P3-5 + P3-15 + P3-15+
P1 + P2 + P3 <= 2000
P1 + P2 + P3 >= 1000
3P1 – 2P2 >=0
P1 + P2 -0.5P3 = 0
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