Problem 1:
The Electrocomp Corporation manufactures two electrical products: air conditioners and large fans. The assembly process for each is similar in that both require a certain amount of wiring and drilling. Each air conditioner takes 3 hours of wiring and 2 hours of drilling. Each fan must go through 2 hours of wiring and 1 hour of drilling. During the next production period, 240 hours of wiring time are available and up to 140 hours of drilling time may be used. Each air conditioner sold yields a profit of $25. Each fan assembled may be sold for a $15 profit.
a) Formulate this LP product mix problem to find the best combination of air conditioner and fans that yields the highest profit.
b) Solve this LP product mix problem by using the graphical approach to solve the LP model you formulated.
a) Solve this LP product mix problem by using Excel Solver or Lindo to solve the model you formulated. Copy and paste your spreadsheet and the Answer report in its entirety from Excel OR your Lindo input and output.
Problem 2:
George Rifkin is considering investing some or all of a $60,000 inheritance in a one-year certificate of deposit paying a fixed 6% or a venture capital group project with a guaranteed 3% return but the potential of earning 10%. George would like to invest the minimum amount necessary to achieve a potential return of at least $4000 and a guaranteed return of at least $2000.
a) Formulate a mathematical model so that George can keep as much money as possible for himself and still meet his investment criteria?
b) Use the graphical approach to solve the model you formulated.
c) Use Excel Solver or Lindo to solve the model you formulated. Copy and paste your spreadsheet and the Answer report in its entirety from Excel OR your Lindo input and output.
Problem 3:
Print Media Advertising (PMA) has been given a contract to market Buzz Cola via newspaper ads in a major southern newspaper. Full-page ads in the weekday editions (Monday through Saturday) cost $2000, whereas on Sunday a full-page ad costs $8000. Daily circulation of newspaper is 30,000 on weekdays and 80,000 on Sundays.
PMA has been given a $40,000 advertising budget for the month of August. The experienced advertising executives at PMA feel that both weekday and Sunday newspaper ads are important; hence they wish to run the equivalent of at least eight weekday and at least two Sunday ads during August. (Assume that a fractional ad would simply mean that a smaller ad is placed on one of the days; that is, 3.5 ads would mean three full-page ads and one half-page ad. Also, assume that smaller ads reduce exposure and costs proportionately.) This August has 26 weekdays and 5 Sundays.
The objective is to determine the optimal placement of ads by PMA in the newspaper during August so as to maximize the cumulative total exposure (as measured by circulation) for the month of August.
a) Formulate the linear programming model for the problem.
b) Use the Graphical method to find the optimal solution. Show all steps.
c) Use Excel Solver or Lindo to solve the model you formulated. Copy and paste your spreadsheet and the Answer report in its entirety from Excel OR your Lindo input and output.