Question #74284

A company manufactures two models of cars, a luxury model and an economy model; the resources requirements for both cars are given below:
Luxury Model Economy Model Total Availability resources
Resources I 10 3 100
Resources II 5 5 60
The unit profit per luxury model is $200 and $150 dollar per economy model
(a) How many luxury and economy models should the company manufacture in order to maximize the profit ?
(b) Discuss the usefulness of linear programming to manager.

Expert's answer

Luxury Economy Total

Resources I 10 3 100

Resources II 5 5 60

The unit profit per luxury model is $200 and $150 dollar per economy model.

(a) To find how many luxury and economy models should the company manufacture in order to maximize the profit we should formulate optimization problem.

Maximize: 200QL + 150QE,

Subject to:

10QL + 3QE = 100,

5QL + 5QE = 60.

From the system of equations above we can find that QE = 2.85 or 3 units, QL = 9.14 or 9 units.

(b) Linear programming is very useful to manager to evaluate possible outcomes of using some resources in production.

Resources I 10 3 100

Resources II 5 5 60

The unit profit per luxury model is $200 and $150 dollar per economy model.

(a) To find how many luxury and economy models should the company manufacture in order to maximize the profit we should formulate optimization problem.

Maximize: 200QL + 150QE,

Subject to:

10QL + 3QE = 100,

5QL + 5QE = 60.

From the system of equations above we can find that QE = 2.85 or 3 units, QL = 9.14 or 9 units.

(b) Linear programming is very useful to manager to evaluate possible outcomes of using some resources in production.

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