Question

A donut shop has a production function given by q = 50k1/3l1/2, where q is the number of donuts produced per hour, k is the number of donut fryers (which is fixed at eight in the short run), and l is the number of employed workers. how many donuts can be produced per hour with four workers in the short run?

Answer 1

Fellow exo-l, I hope this is what you meant by your question, it's a bit vague given that your question q = 50k1/3l1/2. So, I assumed that's what you meant. If not, please tell me and I can edit it again.

`q = 50k ((1)/(3)l)( (1)/(2) ) \\ q = (50 * 8)( (1)/(3) * 4)( (1)/(2) ) \\ q = 400 * (4)/(3) * (1)/(2)`

`q = 400 * (4)/(3) * (1)/(2) \\ q = 400 * (4)/(6) \\ q = 266 (2)/(3)`
A: 267 donuts can be produced.

Hope this helps. - M