CMP $360-$ Operations ResearchChapter $11$: Goal Programming $($Lapin and Whisler$)$ProblemProblem $11-19$ A mutual fund manager wants to determine the level of future purchases tobe made in the categories that follow:Growth Income New Issues WarrantsExpected appreciation $15\%10\%20\%15\%$Loss exposure $20\%5\%30\%40\%$Avg. holding time $($yrs$)21\mathrm{.}3\mathrm{.}1$Brokerage cost $1\%\mathrm{.}5\%2\%5\%$There is $$1,000,000$ to invest, and no more than half of the funds may be invested in any singlecategory$.$ The following goals must be met:Goal $1$: At least $$140,000$ in annualized price appreciationGoal $2$: Total potential loss exposure no greater than $$200,000$Goal $3$: Average portfolio holding time no greater than $1\mathrm{.}5$ yearsGoal $4$: Total brokerage cost not to exceed $$15,000$These goals are listed in decreasing priority. The manager uses penalty points of $5,3,2,$ and $1$for violating the respective goals. Formulate and solve this as a goal program.