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

R3 HP6 Selling price $ 120 $ 180 Variable manufacturing costs per unit $ 72 $ 120 Variable marketing costs per unit $ 18 $ 42 Budgeted total fixed overhead costs $350,000 $550,000 Hours required to produce 1 unit on the regular machine 1 0.5 The following additional information is available:

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

b. Pendleton has no capacity constraint on the high-precision machine.

c. Ofthe $550,000 budgeted fixed overhead costs ofHP6, $360,000 is for lease payments for the high-precision machine. This cost is charged entirely to HP6 because Pendleton uses the machine exclusively to produce HP6. The leasing agreement for the high-precision machine can be cancelled at any time without penalties.

d. All other fixed overhead costs cannot be changed.
Required 1. What product mix—that is, how many units of R3 and HP6—will maximize Pendleton’s operating income?
2. Suppose Pendleton can increase the annual capacity of the regular machine by 15,000 hours at a cost of $180,000? Should Pendleton increase the capacity of the regular machine by 15,000 machine-hours? By how much will Pendleton’s operating income increase?
3. Suppose that the capacity of the regular machine 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 $144 per unit. S3 is exactly like R3 except that its variable manufacturing costs are $84 per unit. What product mix should Pendleton choose to maximize operating income?