Find two positive numbers such that the sum of the first and twice the second is 56 and whose product is a maximum
1 answer:
Let
x-------> the first number
y-------> the second number
P-----> product
we know that
x+2y=56----------> 2y=56-x-----> y=28-0.5x------> equation 1
P=x*y----> equation 2
substitute equation 1 in equation 2
P=x*[28-0.5x]-----> P=28x-0.5x²
using a graph tool
see the attached figure
the vertex is the point (28,392)
that means
for x=28
the product is 392 (maximum)
find the value of y
y=28-0.5x----> y=28-0.5*28----> y=14
the answer is
the numbers are 28 and 14
x-------> the first number
y-------> the second number
P-----> product
we know that
x+2y=56----------> 2y=56-x-----> y=28-0.5x------> equation 1
P=x*y----> equation 2
substitute equation 1 in equation 2
P=x*[28-0.5x]-----> P=28x-0.5x²
using a graph tool
see the attached figure
the vertex is the point (28,392)
that means
for x=28
the product is 392 (maximum)
find the value of y
y=28-0.5x----> y=28-0.5*28----> y=14
the answer is
the numbers are 28 and 14
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Answer:
Margarita gastó <u>$40.43.</u>
Step-by-step explanation:
Tenemos la siguiente información.
<u>km recorridos por Margarita</u>
42 km - ciudad
387 km - autopista
<u>Rendimiento del carro</u>
1 galon cada 28 km - ciudad
1 galon cada 36 km - autopista
Hacemos el siguiente factor de conversión
<u>Ciudad</u>
<u>Autopista</u>
Ahoa, se sabe que 1 galon cuesta $3.30. Por lo tanto, el costo de viaje será:
Total galones = 1.5 + 10.75 = 12.25 galones
Total costo = 3.30*12.25 = $40.43.
Espero te haya servido!