Apple produces iPhones using capital and labor according to the production function

Q^S= (1/64)K^0.75L^0.5

where Q^Sis annual production, K is the annual number of hours of capital used and L is the annual number of hours of labor used.

Labor's hourly wage is $40 and capital's hourly rental rate is $240.

As it turns out, based on these facts, the marginal cost (MC) of producing an iPhone is as follows:

MC = 5120/(Q^0.2).(The S superscript is omitted, but the Q here is supply.)

This is the marginal costequationas it depends on Q.Notice that MC falls when Q rises because iPhone production has increasing returns to scale (RTS) in production.RTS = 1.25 (the sum of the exponents 0.75 and.50).So, production has economies of scale (EOS) of 0.8.With this cost structure in production, Apple can satisfy the entire market demand for iPhones, and it has a monopoly in iPhone production and sales.

The demand curve Apple faces for iPhones is

Q^D= 960,000 - 600P

where P is the iPhone's price.

Q = ___100,000___________

Given that W = $20 and R = $120, this means that L = 4K is always optimal for Apple. Substituting 4K for L into the production function, gives us back total output Q = (1/32)K1.25. Now, using the Q you got in #3 above , what is K?