Question

An automotive plant makes the Quartz and the Pacer. The plant has a maximum production capacity of 1200 cars per week, and they can make at most 600 Quartz cars and 800 Pacers each week. If the profit on a Quartz is $500 and the profit on a Pacer is $800, find how many of each type of car the plant should produce.

Answer 1

To determine the number of Quartz and Pacer cars the plant should produce, set up a system of equations based on the given information and solve the linear programming problem.

Step-by-step explanation:

To determine how many Quartz and Pacer cars the plant should produce, we need to set up a system of equations based on the given information.

Let x be the number of Quartz cars produced and y be the number of Pacer cars produced:

1. We know that the total number of cars produced should not exceed the maximum production capacity of 1200 cars per week, so we have the constraint: x + y <= 1200
2. We also know that the plant can produce at most 600 Quartz cars, so we have the constraint: x <= 600
3. Similarly, the plant can produce at most 800 Pacers, so we have the constraint: y <= 800

The objective is to maximize the profit, which is given by the function P(x, y) = 500x + 800y.

Solving this linear programming problem will give us the optimal values of x and y, which represent the number of Quartz and Pacer cars the plant should produce

Answer 2

x=400 and y=800

Step-by-step explanation:

let x be the Quartez and y is Pacer

x+y≤1200 ( maximum production capacity of 1200 cars per week)

0≤x≤600

0≤y≤800

profit : 500x+800y

at a point : x=0 y=800

profit=500x+800y ⇒ 500(0)+800(800)=640000

profit= 500(600)+0=300000 wen x=600(max), y=0

Profit=500(600)+800(600)= 780000

profit =500(400)+800(800)=840000 this is the max profit when

x=400 and y=800