Question

The automobile assembly plant you manage has a Cobb-Douglas production function given by P = 10x^0.5y^0.5 where P is the number of automobiles it produces per year, x is the number of employees, and y is the daily operating budget (in dollars). Assume that you maintain a constant work force of 140 workers and wish to increase production in order to meet a demand that is increasing by 100 automobiles per year. The current demand is 800 automobiles per year. How fast should your daily operating budget be increasing?

Answer 1

Given, product function, P= 10 x 0.5 yos = 10 fx ry. Current production , P=800 automobiles year. number of employees, x=140 (constant P=10 rx ry. 800=10 Vi4o ry 800 = 54 lovigo - vy y = (lo ) 320 640 800x800 4 01140 - 10x10x140 - Current budget daily operating budget 4= 320 - equo Rate of change of production - dp. (1068 Fy) de love. In de la of 1032 - qe ry}

given, rate of change of production, de 2100 1002 to To 100 (21320) To 140 V7 dy – 20/320 SV 140x76 1). dy - 20 (0.571) =11:42.), de = 11-42 Daily operating budget be increasing at a rate 11:42 dollars per year.