A firm is successfully cost-minimizing while producing their desired output level. Each piece of capital costs $9 to rent by the hour and each worker is paid $7 per hour.

The firm's MPL is equal to 49, and MPK is equal to ____

A shortage of rental capital causes the cost of renting capital to rise to $14 per hour. Assume there is no change to the wages paid to workers. To continue minimizing their cost, the firm should switch to a new production method that uses ____ workers and ____ pieces of capital.

For both blanks, choose from: more, fewer, the same number of.

Suppose a firm is currently using the production function q(L,K)=LK2q(L,K)=LK2, where each workers' wage is $11 and each piece of capital costs $43 to rent. The firm would like to produce 100 units of output at the lowest cost possible. You've been provided with the following equations for MPL and MPK:

MPL=K2MPL=K2 and MPK=2LKMPK=2LK

To produce 100 units of output at the lowest cost, the firm should use ___ units of L and ___ units of K. Round to the nearest integer, if necessary.

Their total cost of producing 100 units of output is $ ___. . Round to the nearest integer, if necessary.

Please show your work.