Please show all work.

Dwayne Johnson owns a company, Rock Muscle that manufactures two types of protein shakes: Rock Regular and Rock EXTREME. Rock Regular is manufactured on a regular machine, but Rock EXTREME must be manufactured on both the regular machine and an "extreme' machine. The following information is available: Additional information includes the following: a) Rock Muscle faces a capacity constraint on the regular machine of 75,000 hours per year. b) The capacity of the 'extreme' machine is not a constraint (it is 'extreme' after all). c) The $820,000 of budgeted fixed costs of Rock Regular relate to maintaining the capacity of the regular machine. d) The $1,000,000 budgeted fixed overhead costs of Rock EXTREME are attributable to maintaining the capacity of the 'extreme' machine. Of that total, $800,000 are lease payments for the 'extreme' machine and $200,000 are depreciation of the part of the factory dedicated to the Rock EXTREME production line. This cost is charged entirely to Rock EXTREME because Rock Muscle uses the machine exclusively to produce it. The company can cancel the lease agreement for the 'extreme' machine at any time without penalties. e) All other overhead costs are fixed and cannot be changed. What product mix - that is, how many units of Rock Regular and Rock EXTREME -will maximize the company's operating income? Show your calculations. Now suppose Rock Muscle can increase the annual capacity of its regular machines by 20,000 machine-hours at a cost of $450,000. What product mix will maximize the company's operating income with this increased capacity and by how much will the company's operating income increase or decrease with this new product mix? Compare with the previous question/scenario and show your calculations