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5. A health-food business would like to create a high-potassium blend of dried fruit in the form
of a box of fruit bars. It decides to use dried apricots, which have 407 mg of potassium per
serving, and dried dates, which have 271 mg of potassium per serving.
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The company can purchase its fruit through www.driedfruitbaskets.com in bulk for a
reasonable price. Dried apricots cost $3.33/serving and dried dates cost $2/serving. The company
would like the box of bars to have at least the recommended daily potassium intake of about
4700 mg, but would like to keep it under twice the recommended daily intake. In order to
minimize cost, how many servings of each dried fruit should go into the box of bars?
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Objective Function:
Constraints:
Corner Points & Answer:

Respuesta :

Thus, the values corresponding to the function and constraints will be:

Objective Function:[tex]C=3.33X+2.00Y[/tex]

Constraints:[tex]407X+271Y\geq 4700\\407X+271Y\leq 9400[/tex]

We begin by defining the variables. Let call:

X = of servings of dried apricots

Y= of servings of dried dates

For apricots, there are 3 servings in one pound. This means that the cost per serving is $9.99/3 = $3.33. The cost for X:

[tex]3.33X[/tex]

For dates, there are 4 servings per pound. This means that the cost per serving is $7.99/4=$2.00. The cost for Y:

[tex]2.00Y[/tex]

The total cost would be:  

[tex]C=3.33X+2.00Y[/tex]

Product must contain at least 4700mg of potassium

[tex]407X+271Y\geq 4700\\407X+271Y\leq 9400[/tex]

So now with the equations set it is possible to see that the desired values are between 9400 and 4700. Then using the critical points X=0, Y=0 for the two given equations. This will inform the points of interest for X and Y if this analysis is needed for the exercise.

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