4. Formulate only, the following problem. a) Three new products are to be produc

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 will 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

LP Formulation:

Decision variables: Three products a,b,c

a1 = units of product a to be produced, and sold at $ 17/unit

a2 = units of product a to be produced, and sold at $ 15/unit

b = units of product b to be produced, and sold at $ 10/unit

c1 = units of product c to be produced, and sold at $ 20/unit

c2 = units of product c to be produced, and sold at $ 18/unit

c3 = units of product c to be produced, and sold at $ 9/unit

Objective: Maximize 17a1 + 15a2 + 10b + 20c1 + 18c2 + 9c3

Constraints:

a1 + a2 + b + c1 + c2 + c3 >= 1000

a1 + a2 + b + c1 + c2 + c3 <= 2000

a1 + a2 >= (2/3)*b

a1 + a2 + b = (1/2)*(c1 + c2 + c3)

a1 <= 12

c1 <= 5

c2 <= 15

c3 <= 2000

a1, a2, b, c1, c2, c3 >= 0

Related Questions

Navigate

• Browse (All)
• Browse 4
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.