Question

Zen Inc. manufactures two types of products, the G.1 and the T.1 models. The manufacturing process consists of two principal departments: production and assembly. The production department has 58 skilled workers, each of whom works 7 hours per day. The assembly department has 25 workers, who also work a 7-hour shift. On an average, to produce a G.1 model, Zen Inc. requires 3.5 labor hours for production and 2 labor hours for assembly. The T.1 model requires 4 labor hours for production and 1.5 labor hours in assembly. The company anticipates selling at least 1.5 times as many T.1 models as G.1 models. The company operates five days per week and makes a net profit of $130 on the G.1 model, and $150 on the T.1 model. Zen Inc. wants to determine how many of each model should be produced on a weekly basis to maximize net profit. Formulate the problem.Let the number of G.1 product produced each week be G.Let the number of T.1 product produced each week be T.Formulate the problem.MaxabG +Spell checkTsubject toSpell checkG +Spell checkT ?Spell check(production labor constraint)Spell checkG +Spell checkT ?Spell check(assembly labor constraint)T ?Spell checkG (constraint reflecting demand)G, T ?Spell check(non-negativity conditions)

Answer 1

Step-by-step explanation:

Below is the problem formulation:

Workers:

Production dept. — 58

Assembly dept. — 25

Available work hours each day for each employee per Department:

Production dept. — 7

Assembly dept. — 7

Average Required Labor Hours per Model:

G.1— Production 3.5; Assembly 2

T.1— Production 4; Assembly 1.5

Net Profit per Model

G.1— $130

T.1— $150

Constraints:

For Labor Hours:

Production

i) 3.5G ≤ 7

ii) 4T≤ 7

Assembly

i) 2G ≤ 7

ii) 1.5T ≤ 7

Objective function: Max Z= 130G+ 150T