Lelime Precision Tools makes cutting tools for metalworking operations. It makes two types of$$ tools: A$6,$ a regular cutting$$ tool, and$$ EX$4,$ a$$ high$-$precision cutting tool. A$6$ is manufactured on a regular$$ machine, but EX$4$ must be manufactured on both the regular machine and a$$ high$-$precision machine. The following information is$$ available:

Requirement $1-$ What product mixminus that $$is$,$ how many units of A$6$ and EX$4$ will maximize Lelime$\text{'}$s operating$$ income? Show your calculations.

Requirement $2-$ Suppose Lelime can increase the annual capacity of its regular machines by $16,000$machine$-$hours at a cost of $$80,000.$ Should Lelime increase the capacity of the regular machines by $16,000$ machine$$ hours? By how much will Lelime$\text{'}$s operating income increase or$$ decrease? Show your calculations.

Requirement $3-$ Suppose that the capacity of the regular machines has been increased to $66,000$ hours. Lelime has been approached by Ward Corporation to supply $24,000$ units of another cutting$$ tool, V$2,$ for $$180$ per unit. Lelime must either accept the order for all $24,000$ units or reject it totally. V$2$ is exactly like A$6$ except that its variable manufacturing cost is $$50$ per unit.$($It takes $1$ hour to produce one unit of V$2$ on the regular$$ machine, and variable marketing cost equals $$10$ per$$ unit.$)$ What product mix should Lelime choose to maximize operating$$ income? Show your calculations. Additional information includes the following:

a$.$ Lelime faces a capacity constraint on the regular machine of $50,000$ hours per year.

b$.$ The capacity of the high$-$precision machine is not a constraint.

c$.$ Of the $$475,000$ budgeted fixed overhead costs of EX$4,$ $$275,000$ are lease payments for

the high$-$precision machine. This cost is charged entirely to EX$4$ because Lelime uses the machine

exclusively to produce EX$4.$ The company can cancel the lease agreement for the high$-$precision machine

at any time without penalties.

d$.$ All other overhead costs are fixed and cannot be changed. Begin by calculating the benefit from only selling A$6$ or EX$4.$