Question

20.)

Zen Inc. manufactures two types of products, the G1 and the T1 model airplane. 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 7-hour shifts. On an average, to produce a G1 model, Zen Inc. requires 3.5 labor hours for production and 2 labor hours for assembly. The T1 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 T1 models as G1 models. The company operates five days per week and makes a net profit of $130 on the G1 model, and $150 on the T1 model. Zen Inc. wants to determine how many of each model should be produced on a weekly basis to maximize net profit.

If the numbers of G1 and T1 products produced each week are denoted as G and T respectively, the function that describes Zen, Inc.’s sales prediction for a week is

Answer 1

Number of products Sold:

T ≥1.5G

Maximize Profit Z=150T+130G

Labor Constraint :

A. Labor hours Available:

Production Department :

Number of labor hours available per day =58*7=406

Number of days in a week =5

Number of labor hours available per week =406*5=2030

Assembly Department :

Number of labor hours available per day =25*7=175

Number of days in a week =5

Number of labor hours available per week =175*5=875

B. Labor hours Required;

Labor hours required for G1 model:

Labor hours required at Production Department=3.5G

Labor hours required at Assembly Department=2G

Labor hours required for T1 model:

Labor hours required at Production Department=4T

Labor hours required at Assembly Department=1.5T

Total labor hours required at Production Department =3.5G+4T

Total labor hours required at Assembly Department =2G+1.5T

Constraint:

Labor hours Required ≤ Labor hours Available

Production Department’s Labor constraint

3.5G+4T ≤2030

Assembly Department’s Labor constraint

2G+1.5T ≤875

The Functions:

Maximize Profit Z=150T+130G

Constraints:

3.5G+4T ≤2030

2G+1.5T ≤875

T ≥1.5G

Additional Solution provided for the student ,but not asked in the question:

ALGEBRAIC SOLUTION:

10.5G+12T=6090

16G+12T=7000

5.5G=7000-6090=910

G=910/5.5=165

T=(2030-3.5G)/4=363

T> 1.5G

Hence,

T=363

G=165

Profit=150T+130G=150*363+130*165=$75,900