Question

7. (5 points wants to hire typists and/or use computers to type up class notes. Each typist costs $10 an hour and each typist needs to work with a computer, which costs $5 an hour to use. Each typist can type up and organize 10 pages an hour. Therefore, the production function can be written as Q=min{10L, 10K}, where is the number of pages typed up, L is the number of hours of typists hired and K is the number of computers rented for use. What is the least costly input combination of labor and computer to type up 100 pages of notes and how much does the input combination cost? (need to get the input combination correct to get partial credits for cost) 8. (5 points) wants to hire typists and/or use a scanning software to minimize the cost of notes. Each typist (with his own computer) can type up and organize 10 pages per hour and costs $15 an hour. The scanning software can transcribe 20 pages per hour and costs $20 an hour. Therefore, the production function can be written as Q = 10L+20K, where is the total number of pages organized, L is the number of hours of typists hired and K is the number of hours the scanning software is used. What is the least costly input combination of labor and capital to type up 100 pages of notes and how much does the input combination cost? (need to get the input combination correct to get partial credits for cost)

Answer 1

solution 1 : = min { lob, lokļ ; w= $other loyalty A q= $5/hr . for optimal : 102= lok= a (rent of computer) lou =10 N-JOU Saw'; for de los ; [La lique = 0 ];[x log ] [2=10;K 2107 of times inputs lost = what tocka = /100/10) + (5) (16) ... [cost - $150 golation & Oz 162 +266 ; w= $15 Ihr r=$20/hr. . (wage of scanning software; - 16 = ² slope of iso cost=-o = 28 - - 1 14 Sinie; slope of suost/ > / slope of isoquentl ...only good k will be used for prodesition. So l l = 20K ; for Q= low CE* ] [Ke kheta 5] [Leo] [lzo] Frost - YK - 2015) - $ 200 ] slope of an quant a _de da