Question

A refinery produces both gasoline and fuel oil and sells gasoline for $1/gallon and fuel oil for $0.90/gallon. The refinery can produce at most 600,000 gallons a day, but must produce at least 2 gallons of fuel oil for every gallon of gasoline. At least 150,000 gallons of fuel oil must be produced each day to meet current demands. How much of each type of fuel should produce to maximize daily profits

Answer 1

Answer:

400,000 gallon's of fuel oil

200,000 gallon's of gasoline

Explanation:

Constraint 1: you must produce at least 2 gallons of fuel oil for every gallon of gasoline

So for every three gallons you must have 2 fuel oil and one gasoline.

Thus 600,000/3 = 200,000

200,000 × 2 = 400,000 fuel oil 200,000 × 1 = 200,000 gasoline

Constraint 2: is that at least 150,000 gallons of fuel oil must be produced. 400,000 is greater than 150,000

Answer 2

The refinery should produce 400,000 gallon's of fuel oil and 200,000 gallon's of gasoline to maximize the daily profit margin.

Computation:

First, read the proportion of the fuel oil and gasoline:

The refinery must produce at least 2 gallons of fuel oil for every 1 gallon of gasoline, that there must be the ratio of 2:1 respectively.

According to this in 3 gallons there must be 2 gallon of fuel oil and 1 gallon of gasoline.

So, the total production of 600,000 gallons will be taken in the ratio of 2:1 after taking out one third part for each gallon.

$\begin{aligned}\text{A single gallon}&=\dfrac{600,000}{3}\\&=200,000\;\text{gallons}\end{aligned}$

Now, this 200,000 gallons will be taken as 2 gallon of fuel oil and 1 gallon of gasoline.

Therefore, the total gallons for maximizing the profit will be 400,000 gallons of fuel oil and 200,000 gallons of gasoline.

To know more about ratio and proportion, refer to the link:

https://brainly.com/question/165414