X=24 should be the correct answer
You are given a bond interest of 6% that was given on January 1, 2016, with a face value of $600,000. Also, the market yield for bonds of similar risk, that <span>the market yield for bonds of similar risk and maturity was 7% and </span>the interest is paid semiannually on June 30 and December 31. You are to find the bond value on January 1, 2016. In here, because the yield of the market is above 6%, the bonds will have a discount for bonds less than $600,000.
Cash interest
= 0.06 * $600,000 * 6/12 (because it is done semiannually)
= $18,000
7%/2 = 3.5%
PV of interest at 3.5%
= $18,000 * 6.87396
= $123,731
PV of face at 3.5%
= $600,000 * 0.75941
= $455,646
Value of bond
= PV on interest + PV of face
= $123,731 + $455,646
= $579,377
Thus, the values corresponding to the function and constraints will be:
Objective Function:
Constraints:
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:
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:
The total cost would be:
Product must contain at least 4700mg of potassium
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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