Good Aliens Corporation: We make Good Product, We have Good Machines; It is All Good! Good Aliens Corporations, a famous paper manufacturer on planet Economia is considering expanding its operations in two new plants across the river: plant Alpha () and plant Beta (): Mr. Rho, the production manager, is reviewing a report submitted by his assistant Hans regarding the short-run total product curves for the two plants. Hans estimated the two production functions as follows:

Hans did not provide any additional information. Mr. Rho, who knows calculus, derived the marginal product for both plants as

Mr. Rho also knows that Good Aliens gave him only 10 workers to start up operations in both plants. The question that Mr. Rho is trying to answer is: How much labour should be allocated to plant Alpha and to plant Beta? And, at the best allocation, what is the output produced?