Question

Layton Machining Company (LMC) manufactures two versions of a basic machine tool. custom model, which requires some additional work and slightly higher-grade materials that each product go through two departments, Grinding and Finishing. The process in machine. Total machine capacity in Grinding is 54,000 hours, and in Finishing, total mac department has multiple machines.) Total market demand is limited to 108,000 standard is currently producing 98.000 standard units and 62,000 custom units each month. Cost follow. Total Standard $ 7.00 $ Custom 9.00 Price Less variable costs per unit Material Labor Overhead Contribution margin per unit Fixed costs Manufacturing Marketing and administrative 1.60 1.35 1.85 2.20 2.10 1.60 2.60 2.70 $ $ $ 78,000 39,899 $117, 0.2 0.1 0.3 0.4 Grinding machine hours per unit Finishing machine hours per unit Grinding machine hours used Grinding machine hours available Finishing machine hours used Finishing machine hours available Quantity produced Maximum demand Profit 38,280 54,000 34,600 35,000 98,000 108,000 $ 266,000 62,000 128,eee Required: a. What is the optimal production schedule for LMC? In other words, how many standard units a produce each month to maximize monthly profit? b. If LMC produces at the level found in requirement (a), how much will monthly profit increase o g p ] x W) NT

Answer 1

Layton Machining Company
Requirement a
Standard units		108000
Custom units		60500
Layton should produce 100,000 Standard units and 50,000 Custom units. First, compute the
contribution margins per hour on the machine for the two products:
Standard (Grinding machine): ($2.20 ÷ 0.2) = $110 per hour
Standard (Finishing machine): ($2.20 ÷ 0.1) = $22.00 per hour
Custom (Grinding machine): ($2.70 ÷ 0.3) = $9.00 per hour
Custom (Finishing machine): ($2.70 ÷ 0.4) = $6.75 per hour
Because Standard has a higher contribution margin per unit of both constraining resources, Layton
should produce up to demand (108,000 units) assuming machine capacity is available. It requires
21,600 grinding hours to produce 100,000 Standard units (= 0.2 hours per unit × 108,000 units)
and 10,800 finishing hours (= 0.1 hours per unit × 108,000 units). This leaves 32,400 grinding
hours (= 54,000 hours available less 21,600 hours for Standard production) and 24,200 finishing
hours (= 35,000 hours available less 10,800 hours for Standard production) to produce Custom
units. Each Custom unit requires 0.3 hours of grinding machine time and 0.4 hours of finishing
machine time. The company can produce 108,000 Custom units with the grinding machine
constraint (= 32,400 ÷ 0.3 hours per unit) or 60,500 units (= 24,200 ÷ 0.4 hours per unit) with the
finishing machine. Therefore, the company can only produce 60,500 Custom units.
Requirement b
Increases profits by
The production of 108,000 Standard units and 60,500 Custom units leads to profits of $283,950 (=
108,000 × $2.20 + 60,500 × $2.70 − $117,000). The current production schedule of 98,000 Standard
units and 62,000 Custom units yields profits of $266,000 (= 98,000 × $2.20 + 62,000 × $2.70 − $117,000).
Therefore, the optimum production schedules increases profits by$17,950 (= $283,950 − $266000).