An invester is considering three types of invertments: a high$-$risk venture into oil leases with a potential retum of $15\%,$ a medium$-$risk investment in bonds with a $9\%$ return, and a relatively safe slock investment with $a5\%$ return. He has $$50,000$ to invest. Bocause of the risk, he will limit his investment in oil leases and bonds to $30\%$ and his investment in oil leases and stock to $56\%.$ How much should he invest in each to maximize his retum, assuming investrnent returns ase as expected?

a$)$ Define the variables. Be specific with descriptive words.

$x=$

$y=$

$z=$

b$.)$ Clearly state the constraints $($all inequalities$)$ related to the fasible region.

c$.)$ State the objective furetio

d$.)$ Set up the initial simplex matrix necded to solve the lines progranuning problera using the Simplex Method.

c$.)$ Perform all pivots nocessary using row operations to transform the marrix unail the solution is fasilhle.

sxyaricy?