Question

A car company produces 2 models, model a / b . Long-term projections indicate an expected demand of at least 100 model a cars and 80 model b cars each day. Because of limitations on production capacity, no more than 200 model a cars and 170 model b cars can be made daily. To satisfy a shipping contract, a total of at least 200 cars much be shipped each day. If each model a car sold results in a $2000 loss, but each model b car produces a $5000 profit , how many of each type should be made daily to maximize net profits?

Answer 1

Answer: Maximum Profit:$790000

Model a: 30 cars

Model b=170 cars

But according to the demand 200 model a car and 170 model b cars to be manufactured and profit of company is $450000 .

Solution:

Let the company makes x units of car A per day

and y units of car B per day.

x ≤ 200

y≤ 170

x +y ≥ 200

Let the profit function is Z.

Z= -$2000x+$5000y

feasible reason is bounded by

A(30,170)

B(200,170)

C(200,0)

On putting these values in the profit function A(30,170)

Z= -$60000+$850000

Z=$790000

B(200,170)

Z= -$400000+$850000

Z=$450000

C(200,0)

Z=-$400000

It is clear that profit of company maximizes only if it manufacture 30 cars of model A and 170 cars of model B.

But according to the demand 200 model a car and 170 model b cars to be manufactured.

Hope it helps you.