Calculas This is a simple question....What is meant by \"equate to 0\"?? Please
ID: 2833966 • Letter: C
Question
Calculas
This is a simple question....What is meant by "equate to 0"?? Please show me all steps in equating to 0.
Solving for Efficient Production:
? Rearrange Production Function:
Q = 2 L.5 K.5 = 12 units
L.5 = 6 / K .5
L = 36 / K
? Substitute for L in Total Cost:
TC = $120 36 K-1 + $50 K = $4320 K-1 + $50 K
Differentiate: deltaTC = -4320 K-2 + 50
deltaK
Equate to 0 and Solve for K: K = 9.295..............I am confused as to how to equate to 0 here
Then L = 36 / 9.295 = 3.873
? Minimum Total Cost of Producing 12 Units = $929.52:
Total Cost = $120 3.873 + $50 9.295
Explanation / Answer
deltaTC = -4320 K-2 + 50 =0
therefore k-2=50/4320 or k2 =4320/50 (taking reciprocal both sides )
k=sqrt(86.4) =9.295
we have deferentiated here because we want the minimum value of cost ...on deferentiating any expression containing any variable (in this case "k") and equating the variable to zero we get that value of variable which gives min value of expression ( in this case the total cost) ..thus k has been substituted to find "L" and thus to find total min cost