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 .

answer: 193

explanation:

200-7 = 193

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.