Answer:
the answer is 12 gallons
Step-by-step explanation:
make fractions improper:
9/8 and 25/2
make them have a common denominator:
9/8 and 100/8
to make a whole gallon but what you do to one side you do to the other:
9/8-1/8=8/8
100/8-1/8=99/8
divide 99/8:
12.375
round down:
12
You do 12 time 2 the 8 times 2 and you can add 15 and 10 and the subtract
The relationship between profit and revenue is:
Profit = Revenue - Total Cost
Since the cost is given as a function, the equation will be substituted as
Profit = Revenue - (3,250 + 5x + 0.1x²)
Now, the revenue is a linear graph because it is the number of pairs multiplied the fixed rate. So, the slope is constant.
Revenue = 110x --> this is the function for revenue
Thus, the equation for profit would be
Profit = 110x - 3,250 - 5x - 0.1x²
P = -0.1x²+105x-3,250 --> this is the function for profit
Now, to find the minimum value of x to make profit, differentiate P with respect to x and equate to 0.
dP/dx = 0 = -0.2x + 105
x = 525
Thus, the Gymnast Clothing should manufacture at least 525 pairs in order to make profit.
Use Pythagoras:
x² = (8.5)² + (5)²
x = √[(8.5)² + (5)²]