LP1

A small company makes only two products with the following two production constraints representing two machines and their maximum availability:

2x + 3Y <=18

2X + Y <=10

where:

X = number of units of first product

Y = number of units of second product

REQUIRED:

If the profit equation is Z = 4X + 2Y, what is the maximum possible profit?

LP2

Golden Hawk Manufacturing seeks to maximize the profits on its three products, for which the following data are available:

                                      A      B      C                 
Contribution margin per unit         $2     $5     $4              
                                                            Total 
Production requirements                                   capacity 
      hours in each department:                           (in hours) 
Assembly                              2      3      2       30,000 
Painting                              1      2      2       38,000 
Finishing                             2      3      1       28,000

REQUIRED:

a. Set up the objective function and constraints for the linear programming problem that will maximize Golden Hawk's profits.

b. Use Lindo to determine the optimal production level for Golden Hawk.

LP3

Jenlock Mill Co. produces two grades of interior plywood from fir and pine lumber. The firm and pine lumber can be sold as saw lumber or used in the plywood.

To produce the plywood, thin layers of wood are peeled from the logs in panels and the panels are glued together to form plywood sheets and then dried. The peeler can peel enough panels to produce 300,000 sheets of plywood in a month. The dryer has a capacity of 1,200,000 minutes for the month. The amount of lumber used and drying time required for each sheet of plywood by grade are shown below:

                       Grade A Sheets    Grade B Sheets   
Fir (in board feet)           18                15        
Pine (in board feet)          12                15        
Drying time (in minutes)       4                6

The only restrictions on the production of fir and pine lumber is the capacity of the mill saws to cut the logs into boards. These saws have a capacity of 500,000 board feet per month regardless of the species.

Jenlock has the following quantities of lumber available for July production:

          Board feet   
Fir       2,700,000 
Pine      3,000,000

The contribution margins for each type of output are:

Fir                $0.20 per board foot  
Pine               $0.10 per board foot  
Grade A plywood    $2.25 per sheet       
Grade B plywood    $1.80 per sheet

The demand in July for plywood is expected to be a maximum of 80,000 sheets for Grade A and a maximum of 100,000 sheets for Grade B. There are no demand restrictions on pine and fir.

Jenlock uses a LINDO to determine the production quantities of each product. Formulate the problem and generate a LINDO solution for this problem.