Question 1098327: A coffee merchant sells two blends of coffee. Each pound of blend A contains 80% Mocha Java and 20% Jamaican and sells for $2 a pound. Each pound of blend B contains 35% Mocha Java and 65% Jamaican and sells for $2.25 a pound. The merchant will try to sell the amount of each blend that maximizes her income. Let X be the number of pounds of blend A and Y be the number of pounds of blend B.
In the situation above, the objective function is
A.) 1000x + 600y B.) 0.80x + .20y C.) 2x + 2.25y D.) 2.25x + 2y
Since the merchant above has available 1000 pounds of Mocha Java, one constraint that must be satisfied is:
A.) 0.35x+0.65y >= 1000 B.) .08x + 0.35y <= 1000 C). .8x + .035y >= 1000
D.) 0.8x+0.2y <= 1000
Since the merchant above has available 600 pounds of Jamaican, one constraint that must be satisfied is:
A.) 0.35x+0.65y >= 600 B.) 0.2x+.65y <= 600 C.) 0.35x + .065y <= 600
D.) 0.2x + 0.65y >= 600
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! blend A is 80% mocha java and 20% jamaican
blend B is 35% mocha java and 65% jamaican.
you have 1000 pounds mocha java available and you have 600 pounds jamaican available.
your constraint functions are:
.8x + .35y <= 1000
.2x + .65y <= 600
your objective function is 2x + 2.25y.
this is what you want to maximize.
not shown are that x and y have to be greater than or equal to 0.
your graphical solution is shown below:
in this graph, the area of the graph that is NOT shaded is your region of feasibility.
the corner points of the graph are where your maximum revenue will be at.
you evaluate the objective function at these corner points to find the corner point that gives you the maximum revenue.
all constraints must be met at each of the corner points as well.
looking at the graph, the corner points are:
(0,923.077)
(977.778,622.22)
(1250,0)
your revenue at each of these points is:
2076.923
3355.551
2500
your maximum revenue is when you sell 977.778 pounds of blend A and 622.22 pounds of blend B.
when you sell 977.778 pounds of blend A and 622.22 pounds of blend B, your constraints need to be satisfied as well.
mocha java constraints of .8x + .35y must be less than or equal to 1000 pounds.
.8 * 977.778 + .35 * 622.22 is equal to 999.9994 pounds of mocha java used which is at or below the limit of 1000 pounds.
jamaican constraints of .2x + .65y must be less than or equal to 600 pounds.
.2 * 977.778 + .65 * 622.22 pounds is equal to 599.9986 pounds of jamaican used which is at or below the limit of 600 pounds.
note that i graphed the opposite of the inequalities.
this is what allowed me to see that the region of feasibility is the area that is NOT shaded.
looking at your selections, i get the following:
A.) 1000x + 600y B.) 0.80x + .20y C.) 2x + 2.25y D.) 2.25x + 2y
selection C.
Since the merchant above has available 1000 pounds of Mocha Java, one constraint that must be satisfied is:
A.) 0.35x+0.65y >= 1000 B.) .08x + 0.35y <= 1000 C). .8x + .035y >= 1000
D.) 0.8x+0.2y <= 1000
answer should be .8x + .35y <= 1000.
check your selections again to see which one matches this.
i'm guessing selection B, but you have .08x rather than .8x.
hopefully that's a typo.
Since the merchant above has available 600 pounds of Jamaican, one constraint that must be satisfied is:
A.) 0.35x+0.65y >= 600 B.) 0.2x+.65y <= 600 C.) 0.35x + .065y <= 600
D.) 0.2x + 0.65y >= 600
selection B.
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