27. manufacturing a shoe manufacturer makes outdoor
and indoor soccer shoes. there is a two-step process for
both kinds of shoes. each pair of outdoor shoes requires
2 hours in step one and 1 hour in step two, and produces
a profit of $20. each pair of indoor shoes requires 1 hour in
step one and 3 hours in step two, and produces a profit
of $15. the company has 40 hours of labor available per
day for step one and 60 hours available for step two.
what is the manufacturer's maximum profit? what is
the combination of shoes for this profit?

1.5%

step-by-step explanation:

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form