1) Jim is planning to invest between $12,000 and $15,000 in two types of investment: investment 1 yields 6% and investment 2 yields 8%. Because of tax laws, he should invest between 40% and 60% of his total investment in investment 1 and no more than $8,100 in investment 2. How much should he invest and how should that amount be allocated to the two investments?
a) describe the components (decision variables, objective function, and constraints) in the context of this problem.
b) write the mathematical formulation of the problem.
c) solve the problem graphically and explain the optimal allocation of investment fund to the two investments.
d) In an Excel workbook, solve the problem by using the Solver.
2) John must work at least 20 hours a week to supplement his income while attending school. He has the opportunity to work in two retail stores. In store 1, he can work between 5 and 12 hours a week, and in store 2, he should work at least10 hours a week. Both stores pay the same hourly wage. In deciding how many hours to work in each store, John wants to base his decision on work stress. Based on interviews with present employees, John estimates that, on an ascending scale of 1 to 10, the stress factors are 8 and 6 at stores 1 and 2, respectively. Because stress mounts by the hour, he assumes that the total stress at each store by the end of the week is proportional to the number of hours he works in the store. How many hours should John work in each store?
a) describe the components (decision variables, objective function, and constraints) in the context of this problem.
b) write the mathematical formulation of the problem.
c) solve the problem graphically and explain the optimal number of hours John should work at each store.
d) In an Excel workbook, solve the problem by using the Solver.
3) A large department store operates seven days a week. The manager estimates that the minimum number of salespersons required to provide prompt service is 12 for Monday, 18 for Tuesday, 20 for Wednesday, 28 for Thursday, 32 for Friday, and 40 each for Saturday and Sunday. Each salesperson works five consecutive days and takes two days off. The manager wants to know how many salespersons should be contracted and how their days off should be allocated.
a) describe the components (decision variables, objective function, and constraints) in the context of this problem.
b) write the mathematical formulation of the problem.
c) describe the solutions obtained from the Solver and answer the manager’s questions.
d) In an Excel workbook, solve the problem by using the Solver.