Question

Ficcus Inc. manufactures two types of products, the Gx and the Tx models. The company operates five days per week and makes a net profit of $125 on the Gx model, and $175 on the Tx model. The models are manufactured in two main 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 Gx model, Ficcus Inc. requires 4.5 labor hours for production and 3 labor hours for assembly. The Tx model requires 5.5 labor hours for production and 2.5 labor hours in assembly. The company anticipates selling at least 1.5 times as many Tx models as Gx models. Ficcus 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 Gx product produced each week be G. Let the number of Tx product produced each week be T. Formulate the problem. Max G + T subject to G + T ? (production labor constraint) G + T ? (assembly labor constraint) T ? G (constraint reflecting demand) G, T ? (non-negativity conditions)

Answer 1

gx assembly net profit 125 tx production net profit 175

83workers 7hours a day 58 workers 7hours a day

to produce gx model requires 7.5lab hrs to produce tx model requires 8.0lab hrs

labour hours caluculations labour hours caluculations

per day = 7hrs perday 7 hours

1 week 7*7=49hrs 1 week 7*7=49

1 product =7.5hrs 1 produt =8.0hrs

so 49/7.5=6.53 so 49/8=6.12

in a week gx will produce in a week tx will produce

83*6.53=541.99 units 83*6.12=508.37units

so G=541.99 UNITS IN A WEEK T=508.37 UNITS IN A WEEK