CASE $11-1$ Let There Be Light Lamp Shade Company

Started in Madison, Wisconsin, after the student unrest of the $1960$s had died down, the Let There Be Light Lamp Shade Company served an upscale local market for many years. It designed and built custom lamp shades and lamp globes. In the mid$-1980$s$,$ some architects who had once studied under Frank Lloyd Wright in nearby Spring Green were commissioned to design several large public buildings in Asia. A total of $5,400$ identical lights were to be installed, and the Let There Be Light Lamp Shade Company wished to bid on the work. Terms of sale would include delivery to the foreign port where the buyer would take possession.

Transportation costs would be a hurdle. In the initial design, the shades were cylinders that were $11$ inches high and $11$ inches in diameter and were packed into boxes that were $12$ by $12$ by $12$ inches. $($We refer to these shades as style A$.)$ The packages cost $60$ cents each and weighed $1$ pound each. The shades cost $\backslash (\backslash$$ $4\backslash )$ each to manufacture. They weighed $9$ pounds each and $10$ pounds packaged.

They would be shipped to the Port of Oakland. The land rate to Oakland was $\backslash (\backslash$$ $1,000\backslash )$ per $40-$foot container, without regard to weight, although the weight of the load could not exceed $44,000$ pounds per loaded container because of highway weight restrictions. The interior dimensions of the intermodal container were $8$ feet wide by $8\mathrm{.}5$ feet high by $40$ feet long.

Ocean rates from Oakland to the overseas port were $\backslash (\backslash$$ $22\backslash )$ per ton $(2,000$ pounds$),$ except that the ocean conference used a measurement ton that indicated that for bulky loads every $40$ cubic feet would equal $1$ ton for rate$-$making purposes. $($That is$,$ a shipment weighing, say, $130$ pounds and occupying $80$ cubic feet would cost as though it weighed $4,000$ pounds.$)$ Insurance costs were $2$ percent of the value of the shipment ready to be loaded aboard ship in Oakland. $($This is calculated as all of the company's costs up to this point.$)$

Because of the large size of the order, Let There Be Light Lamp Shade Company realized that it could custom design a shade that, rather than being a cylinder, would be shaped like a cone. The advantage to that was that the shades could be nested. Some padding would be $-$required between the shades, but the nested shades would also help protect each other. However, cutting out material for conical shapes results in waste, so production costs would be higher. Two alternative cone$-$shaped designs were proposed $($referred to as styles B and C$).$

Style B cost $\backslash (\backslash$$ $5\backslash )$ per shade to manufacture and could be shipped nested in packages of six. The package dimensions were $12$ by $12$ by $48$ inches, and when holding six shades, a package weighed $62$ pounds. Each package cost $\backslash (\backslash$$ $2\backslash ),$ and this included padding between the shades.

Style C cost $\backslash (\backslash$$ $6\backslash )$ per shade to make and could be shipped nested in packages of $10.$ The package dimensions were $12$ by $12$ by $50$ inches, and when holding $10$ shades, a package weighed $101$ pounds. Each package cost $\backslash$$$3,$ including padding between the individual shades.

Questions

$1.$ How many style A shades can be loaded into an intermodal container?

$2.$ How many style B shades can be loaded into an intermodal container?

$3.$ How many style $\backslash ($ C $\backslash )$ shades can be loaded into an intermodal container?

$4.$ What are the total costs of delivering the style A shades to the port of importation?

$5.$ What are the total costs of delivering the style B shades to the port of importation?

$6.$ What are the total costs of delivering the style C shades to the port of importation?

$7.$ Which style would you recommend? Why?