Afirmwishestoproduce Q(complement, dash over the letter Q)=150ascheaplyaspossibleusingonlylabor(L)and capital (K) with a relationship explained by the following production technology:Q=15L+ 25K.The prevailing market wage is $w/hr.You will need to work carefully to determine the wage rate but know that the rental rate of capital,r= 50.

a. Find w so that the firm can optimally employ 5 workers and 3 units of capital to produce output: Q(complement)= 150 while still minimizingcosts.Show all work to report w and the total minimum cost associated with this level of production.

b. Suppose it currently costs the firm $300 to produce Q(complement) = 150 units of output optimally while using at least some capital. What's the lower bound on how large the wage can be given these circumstances?

c. Now suppose the wage rate w falls to be strictly lower than the bound you identified in (b).Find the upper bound on the minimum cost to produce Q(complement) = 150. Inotherwords,findthelargestamountthatthecostminimizingfirmwouldbe paying to produce Q(complement)= 150 assuming it is still optimizing after the decrease in w.