Spoonfuls, Inc. manufactures three spoon products made from recycled wood: A soup spoon, a small wooden sampler spoon and a tall drink spoon. Demand for all three products is robust.

Average weekly demand for their $3$ products is listed below. Spoons are sold in packs of $100.$ The data below are for spoon packs, not individual spoons.

Spoonfuls operates specialty wood cutting$/$sanding lathes to manufacture these three products. Because of the wear and tear and saw dust created by their extensive use, at least $2$ lathes are being repaired or being cleaned during most production weeks and therefore, unavailable for use.

Silvia Spooner, Spoonfuls controller and daughter of the founder, is focused on operating profit. She worries that continued lathe downtime is severely lowering weekly profit. She would like to develop a production plan which maximizes weekly operating profit when there are insufficient lathe manufacturing hours to produce that week's demand.

She has collected the following average weekly demand, product costs and lathe production times needed to make a pack of each spoon$-$type. Lathes run, on average, $60$ hours per week.

Assuming there are only $21$ lathes available during next week's production, what spoon$-$type and how many packs should be made first, second, and then third to maximize operating profit at this reduced level of capacity?

Sampler Spoon Soup Spoon Tall Drink Spoon

Ave Weekly Demand $($in packs of $100$ spoons$)3,8402,4002,200$

Selling Price per pack $$7\mathrm{.}50$ $$20\mathrm{.}00$ $$30\mathrm{.}00$

Variable Cost per pack

Wood $$1\mathrm{.}00$ $$4\mathrm{.}00$ $$5\mathrm{.}90$

Labor $$1\mathrm{.}50$ $$3\mathrm{.}00\%5\mathrm{.}40$

Bag $$0\mathrm{.}10$ $$0\mathrm{.}20$ $$0\mathrm{.}30$

Utilities $$0\mathrm{.}40$ $$1\mathrm{.}00$ $$1\mathrm{.}60$

Total Variable Costs $$3\mathrm{.}00$ $$8\mathrm{.}20$ $$13\mathrm{.}20$

$\%$ of Rev $40\%41\%44\%$

Contribution Margin per pack $$4\mathrm{.}50$ $$11\mathrm{.}80$ $$16\mathrm{.}80$

$\%$ of Rev $60\%59\%56\%$

Lathe $($machine$)$ minutes to make $1$ pack $5\mathrm{.}010\mathrm{.}018\mathrm{.}0$

Group of answer choices

a$)$ #$1)$ Sampler Spoon: $3,840$; #$2)$ Soup Spoon: $2,400$; #$3)$ Tall Drink Spoon: $2,200.$

b$)$ #$1)$ Soup Spoon: $2,400$; #$2)$ Sampler Spoon: $3,840$; #$3)$ Tall Drink Spoon: $2,200$

c$)$ #$1)$ Tall Drink Spoon: $2,200$; #$2)$ Sampler Spoon: $3,840$; #$3)$ Soup Spoon: $1,800$

d$)$ #$1)$ Soup Spoon: $2,400$; #$2)$ Tall Drink Spoon: $2,200$; #$3)$ Sampler Spoon: $2,400$

e$)$ #$1)$ Tall Drink Spoon: $2,200$; #$2)$ Soup Spoon: $2,400$; #$3)$ Sampler Spoon: $1,800$

f$)$ There is insufficient information to compute an answer