Answer:
The correct answer is option d.
Explanation:
The production function is given as:
f (L, M) =[tex]5L^{1/2} M^{1/2}[/tex]
The total cost will be
= wL + rM
Here, w is the cost of labor or wages and r is the cost of capital or rent.
The cost of labor is given as $9 per unit and the cost of using machine is $64 per machine.
MPl
= [tex]\frac{dQ}{dL}[/tex]
= [tex]\frac{5}{2}\frac{M}{L}^{1/2}[/tex]
MPm
= [tex]\frac{dQ}{dM}[/tex]
= [tex]\frac{5}{2}\frac{L}{M}^{1/2}[/tex]
[tex]\frac{MPl}{MPm} = \frac{9}{64}[/tex]
[tex]\frac{M}{L} = \frac{9}{64}[/tex]
M = [tex]\frac{9}{64}L[/tex]
f (L, M) = [tex]5L^{1/2} M^{1/2}[/tex]
12 = [tex]5L^{1/2} \frac{9}{64}L^{1/2}[/tex]
12 = [tex]\frac{15L}{8}[/tex]
L = [tex]\frac{96}{15}[/tex]
L = 6.4
M = [tex]\frac{9}{64}\times 6.4[/tex]
M = 0.9
Total cost
= wL + rM
= 6.4 [tex]\times[/tex] 9 + 0.9 [tex]\times[/tex] 64
= 57.6 + 57.6
= $115.2
