A small company produces two goods, swords and plowshares.The company has 100 type alpha employees and 100 type beta employees.If an alpha devotes all his time to producing swords, he can make 4 swords per week.If he devotes all his time to producing plowshares, he can make 20 plowshares per week.A beta can produce either 1 plowshare per week or 1 sword per week.The company wants to produce 413 swords and as many plowshares as it can.How many type betas should it employ at making swords?
A)80
B)0
C)100
D)13
E)None of the above.

Question

Quizplus · Accepted Answer

To maximize plowshare production while still meeting the sword production target, all type alpha employees should be allocated to making plowshares, as they are significantly more efficient at this task. This leaves the sword production to type beta employees. Each alpha can produce 20 plowshares, so their contribution to plowshare production is maximized by not diverting any of them to sword production. Since each beta can produce 1 sword per week, and the company needs to produce 413 swords, all 100 beta employees should be allocated to sword production to meet the target as efficiently as possible.

A Small Company Produces Two Goods, Swords and Plowshares