In an oil mill, they decide to make a mixture from two types of oil: the extra virgin whose price is $4 per liter and the virgin $3 per liter. They have 200 L of extra virgin olive oil and 500 L of virgin olive oil and they also want the cost of the mixed oil to be at least 1500 dollars.The extra virgin olive oil will be e, while the virgin olive oil will be v.a) Set up a system of inequalities that contains the restrictions set out in the problem.The total number of mixed oil is: e + v = m 200 + 500 = 700Considering 4 e + 3 v, the maximum total price of the mixed oil is 2300: 4 ( 200 ) + 3 ( 500 ) = 2300Then, I've formed a system of inequalities { e + v ≤ 700 4 e + 3 v ≥ 1500 I'm not sure if I've transformed the problem into a system correctly.b) Is it possible to meet the conditions if the mixture contains the same amount of the two oils?Since I wasn't sure about my system of equations, I've done the last two questions using 4 e + 3 vI'm taking the max amount of extra virgin oil, 200L, and this is what we get: 4 ( 200 ) + 3 ( 200 ) = 800 + 600 = $ 1400 So, the answer would be 1400 &lt; 1500So, no, it would meet the conditions.c) If they decide to use all the extra virgin oil they have in the mixture, what will be the amount of virgin oil that they should use if they want the cost of the mixture to be $ 1700? 1700 = 4 ( 200 ) + 3 v 1700 − 800 3 = v 300 L = vIf you could help me identify my errors I would greatly appreciate it.

Question

In an oil mill, they decide to make a mixture from two types of oil: the extra virgin whose price is $4 per liter and the virgin $3 per liter. They have 200 L of extra virgin olive oil and 500 L of virgin olive oil and they also want the cost of the mixed oil to be at least 1500 dollars.The extra virgin olive oil will be   e, while the virgin olive oil will be   v.a) Set up a system of inequalities that contains the restrictions set out in the problem.The total number of mixed oil is:  e  +  v  =  m  200  +  500  =  700Considering   4  e  +  3  v, the maximum total price of the mixed oil is   2300:  4  (  200  )  +  3  (  500  )  =  2300Then, I&#039;ve formed a system of inequalities      {                            e          +          v          ≤          700                                      4          e          +          3          v          ≥          1500                        I&#039;m not sure if I&#039;ve transformed the problem into a system correctly.b) Is it possible to meet the conditions if the mixture contains the same amount of the two oils?Since I wasn&#039;t sure about my system of equations, I&#039;ve done the last two questions using  4  e  +  3  vI&#039;m taking the max amount of extra virgin oil,   200L, and this is what we get:  4  (  200  )  +  3  (  200  )  =  800  +  600  =  $  1400  So, the answer would be  1400  &amp;lt;  1500So, no, it would meet the conditions.c) If they decide to use all the extra virgin oil they have in the mixture, what will be the amount of virgin oil that they should use if they want the cost of the mixture to be $  1700?  1700  =  4  (  200  )  +  3  v            1700      −      800        3    =  v  300  L  =  vIf you could help me identify my errors I would greatly appreciate it.

Donavan Mack · Accepted Answer

Your first inequality   e  +  v  ≤  700 is not written correctly, since it would allow the possibility of   (  e  ,  v  )  =  (  600  ,  100  ) which is not possible in this problem.Instead, you will need to write two separate inequalities:  e  ≤  200  v  ≤  500Your cost inequality is correct:   4  e  +  3  v  ≥  1500Your answer to (b) appears to be correct. You correctly decided to use   200 L of both types of oil, which is the maximum allowed in this part of the problem.Your answer to (c) is also correct.

In an oil mill, they decide to make a mixture from two types of oil: the extra virgin whose price is

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