Product mix, special order. (N. Melumad, adapted) Pendleton Engineering makes cutting tools for metalworking operations. It makes two types of tools: R3, a regular cutting tool, and HP6, a high-precision cutting tool. R3 is manufactured on a regular machine, but HP6 must be manufactured on both the regular machine and a high-precision machine. The following information is available.

Additional information includes the following:a. Pendleton 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 $550,000 budgeted fixed overhead costs of HP6, $300,000 are lease payments for the highprecision machine. This cost is charged entirely to HP6 because Pendleton uses the machine exclusively to produce HP6. The lease agreement for the high-precision machine can be canceled at any time without penalties.d. All other overhead costs are fixed and cannot be changed.Required1. What product mix'that is, how many units of R3 and HP6'will maximize Pendleton's operating income? Show your calculations.2. Suppose Pendleton can increase the annual capacity of its regular machines by 15,000 machine-hours at a cost of $150,000. Should Pendleton increase the capacity of the regular machines by 15,000 machinehours? By how much will Pendleton's operating income increase? Show your calculations.3. Suppose that the capacity of the regular machines has been increased to 65,000 hours. Pendleton has been approached by Carter Corporation to supply 20,000 units of another cutting tool, S3, for $120 per unit. Pendleton must either accept the order for all 20,000 units or reject it totally. S3 is exactly like R3 except that its variable manufacturing cost is $70 per unit. (It takes one hour to produce one unit of S3 on the regular machine, and variable marketing cost equals $15 per unit.) What product mix should Pendleton choose to maximize operating income? Show yourcalculations.

R3 HP6 150 100 Selling price Variable manufacturing cost per unit Variable marketing cost per unit Budgeted total fixed overhead costs Hours required to produce one unit on the regular machine 100 60 15 35 $550,000 0.5 $350,000 1.0