Question 1189157: A manufacturer's earnings can be represented by a linear function.
For an order of 60 stand fan, it earns Php. 7,000 and for 100 order,
it earns Php. 15,000.
a, write the linear function
b. how many electric fans must be manufactured to guarantee an earning of Php. 45,000?
c. how much would the manufacturer earn if it accepted an order of 200 electric fans?
d. If the manufacturer has a maximum earning of Php. 75,000 what is the most number of orders of electric fans has it?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! with an order of 60, they make 7000
with an order of 100, they make 15000
the change in what they make is equal to 8000.
the change in the size of the order is equal to 40.
the general form of the equation is y = mx + b
m is the slope.
b is the y-intercept.
the slope is the change in what they make divided by the corresponding change in the number of orders.
that is equal to 8000 / 40 = 200.
the equation becomes y = 200 * x + b.
the y-intercept is the value of y when the value of x is 0.
to find it, replace a and y with their respective corresponding values and solve for b.
i chose 60 orders for 7000 php.
equation becomes 7000 = 200 * 60 + b
solve for b to get:
b = 7000 = 200 * 60 = -5000
equation becomes y = 200x - 5000.
answers to your questions are:
a. write the linear function
y = 200x - 5000
b. how many electric fans must be manufactured to guarantee an earning of Php. 45,000?
replace y with 45000 and solve for x.
45000 = 200x - 5000
add 5000 to both sides of the equation to get:
50000 = 200x.
solve for x to get:
x = 50000/200 = 250.
number of orders required to make 45000 is 250.
c. how much would the manufacturer earn if it accepted an order of 200 electric fans?
y = 200 * x - 5000
replace x with 200 to get:
y = 200 * 200 - 5000
solve for y to get:
y = 35000
order of 2100 will earn 35000.
d. If the manufacturer has a maximum earning of Php. 75,000 what is the most number of orders of electric fans has it?
replace y with 75000 to get:
75000 = 200 * x - 5000
add 5000 to both sides of the equation to get:
80000 = 200 * x
solve for x to get:
x = 80000 / 200 = 400.
maximum number of orders would be 400.
the equation can be graphed.
here's what it looks like.
the equation graphed is y = 200x - 5000.
selected points are in (x,y) format.
x is the number of orders.
y is the amount earned.
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