A furniture manufacturer produces chairs and sofas. Each chair requires 10 yards of fabric, and each sofa requires 20 yards of fabric. The manufacturer has 300 yards of fabric available. To fulfill orders, the number of sofas must be at least twice the number of chairs. The manufacturer earns a profit of $50 on each chair and $80 on each sofa. Let x represent the number of chairs and y represent the number of sofas. Choose the function that represents the manufacturer's profit, P.

Given:

Fabric required for each chair = 10 yards

Fabric required for each sofa = 20 yards.

Total available fabric = 300 yards.

The number of sofas must be at least twice the number of chairs.

Profit on each chair = $50

Profit on each sofa = $80.

To find:

The function that represents the manufacturer's profit, P.

Solution:

Let P represents the manufacturer's profit, x represent the number of chairs and y represent the number of sofas.

Profit on 1 chair = $50

Profit on x chairs = $50x

Profit on 1 sofa = $80

Profit on y sofas = $80y

Total profit = Profit on x chairs + Profit on y sofas

Therefore, the required profit function is .

step-by-step explanation:

12475909

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)