math problem?

Question

Pension fund investments

A pension fund has decided to invest $45,000 in the two high-yield stocks:

Duke Energy Corp with a share price of $14 and yield return of 8%.

Eastman Kodak with a share price of $30 and yield return of 6%.

This pension fund has decided to invest at least 25% of the $45,000 in each of the two stocks. Further, it has been decided that at most 63% of the $45,000 can be invested in either one of the stocks. How many shares of each stock should be purchased in order to maximize the annual yield, while meeting the stipulated requirements? what is the annual yield in dollars for the optimal investment plan?

Answer 1

x = shares of Duke
y = shares of Kodack

14x =/> 11250
14x =/< 28350
30y =/> 11250
30y =/< 28350
x>0
y>0
Yield = 14x(.08) + 30y(.06) = 1.12x + 1.8y

Plot all the connstraints, find the feasible range, and evaluate the yield at each corner of the feasible range. This is a linear algebra problem you should now be able to solve.

Answer 2

63% invested in Duke Energy Corp
37% invested in Eastman Kodak

63% of $45,000 = $28,350 buys 2,025 Duke Energy Corp shares.
37% of $45,000 = $16,650 buys 2,775 Eastman Kodak shares.
Ignoring buying costs.
Annual yield for Duke Energy Corp = 8% of $28,350 = $2,268
Annual yield for Eastman Kodak = 6% of $16,650 = $999.

Total Annual yield = $2,268 + $999 = $3,267 or 7.26%

Answer 3

optimum = more of the 8% return ... & less of the 6% return

max 8% = 63%-25% = 38%

-Investment
Duke will have 38% of $45k invested in it ($17,100)
Kodak will have 25% of $45k invested in it ($10350)

-Shares
Duke: $17100 /14$perShare = 1221.4286 shares
... 1222 shares would take us over the alloted 63%, so we round down to 1221
Kodak: $10350 / 30$perShare = 345 shares

-Yield
Duke: 1221 * .08 = $97.68 per year.
Kodak: 345 * 0.06 = $20.70

Answers
A1: 1221 Duke Shares
A2: 345 Kodak Shares

B: $118.38