Galaxy Industries is a manufacturing company that produces two toy doll models: the Space Ray and the Zapper. The Space Ray can be sold for a profit of $8/dozen and a profit of $5 can be made if a dozen of Zappers are sold. Each figurine is made of plastic, whose availability for production is limited to 1000lbs each week. Furthermore, a maximum of 40hrs are available for production each week. Space Rays require 3mins of production for each dozen produced and 4mins are required to manufacture a dozen Zappers. The marketing department has also notified you that the total number of figurines should not exceed 700 dozens each week and that the total number of Space Rays should not exceed the total number of Zappers by 350 dozens each week. A summary of the requirements for the project is tabulated below.
Constraints Space Ray Zapper Availability [/week]
Plastic [lbs/dozen] 2 1 1000 lbs
Production time [mins/dozen] 3 4 40 hrs
Profit [$/dozen] 8 5
Using a graphical approach, determine the optimal amount of Space Rays and Zappers that need to be produced in order to maximize profits every week. Describe the type of solution you obtained and clearly state your choice of decision variables, objective function as well as constraints