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(60 points) Let There Be Light lampshade company designs and build custom lamps. They are commissioned to build 5,400 identical lights for a client....
1. (60 points)
Let There Be Light lampshade company designs and build custom lamps. They are commissioned to build 5,400 identical lights for a client. They will produce, package and deliver all 5,400 lights to the client. They are considering two different designs.
Style A LampsThe initial design was a cylinder (diameter of the top and bottom are identical). In this design, the shades for the lamps were 11 inches high and 11 inches in diameter. They were packed into boxes that were 12 inches by 12 inches. These are STYLE A lamps. The cost per package for these lamps is $0.60 and the weight is 1 pound. The shades themselves cost $4 to make and they each weigh 9 pounds. In total, the package then weighs 10 pounds (1 for the box and 9 for the shade). This design would ship out of City A. The cost to ship from City A to the client is $1,000 per container (regardless of the weight of the container). Even though weight does not affect cost, you cannot fill the container to a weight more than 44,000 pounds. The container is 40 feet long by 8 feet wide by 8.5 feet high.
Style B LampsThe other option they are considering producing is a cone shaped lamp shade (the diameter of the top is smaller than the diameter of the bottom). The advantage to this option is that it could be nested. Some padding would be required between shades in a box, but the nesting would provide added protection. Cutting this style lamp shade would result in added waste so production costs are slightly higher. Every lamp shade would cost $5 to produce and could be nested in packages of 6. A box with 6 nested lamp shades would be 12 x 12 x 48 inches. The total weight of this package (package plus lamp shades) would be 62 pounds. Each box (package) itself, would cost
$2. This $2 cost includes the box and the additional padding needed.
Style C LampsThe company is considering a third option that would also be nested and a cone shape. This lamp shade would cost $6 to make (per lamp shade) and could be nested in groups of 10. This package of 10 nested lamp shades would be 12 by 12 by 50 inches. This total package (box plus the 10 lamp shades inside) would weigh 101 pounds each. The cost per package, including extra padding, would be $3.
a. How many Style A shades can be loaded into ONE container?b. How many Style B shades can be loaded into ONE container?
c. How many Style C shades can be loaded into ONE container?
d. What is the total cost of delivering Style A shades to the client? (Production PLUS transportation cost)
e. What is the total cost of delivering Style B shades to the client? (Production PLUS transportation cost)
f. What is the total cost of delivering Style C shades to the client? (Production PLUS transportation cost)
g. Which of these three options would you recommend using? Why?
