Problem
Slavin Corporation manufactures two products, Alpha and Delta. Each product requires time on a single machine. The machine has a monthly capacity of 500 hours. Total market demand for the two products is limited to 150 units (each) monthly. Slavin is currently producing 110 Alphas and 110 Deltas each month. Cost and machine-usage data for the two products are shown in the following table, which Slavin managers use for planning purposes:
|
Alpha
|
Delta
|
Total
|
|
Price
|
$
|
120
|
|
$
|
150
|
|
|
|
|
|
|
Less variable costs per unit
|
|
|
|
|
|
|
|
|
|
|
|
Material
|
|
20
|
|
|
35
|
|
|
|
|
|
|
Labor
|
|
26
|
|
|
37
|
|
|
|
|
|
|
Overhead
|
|
14
|
|
|
14
|
|
|
|
|
|
|
Contribution margin per unit
|
$
|
60
|
|
$
|
64
|
|
|
|
|
|
|
Fixed costs
|
|
|
|
|
|
|
|
|
|
|
|
Manufacturing
|
|
|
|
|
|
|
$
|
8,000
|
|
|
|
Marketing and administrative
|
|
|
|
|
|
|
$
|
5,000
|
|
|
|
|
|
|
|
|
|
$
|
13,000
|
|
|
|
Machine hours per unit
|
|
2.0
|
|
|
2.5
|
|
|
|
|
|
|
Machine hours used
|
|
|
|
|
|
|
|
495
|
|
|
|
Machine hours available
|
|
|
|
|
|
|
|
500
|
|
|
|
Quantity produced
|
|
110
|
|
|
110
|
|
|
|
|
|
|
Maximum demand
|
|
150
|
|
|
150
|
|
|
|
|
|
|
Profit
|
$
|
640
|
|
|
|
|
|
|
|
|
Required:
a. What is the optimal production schedule for Slavin? In other words, how many Alphas and Deltas should the company produce each month to maximize monthly profit?
b. If Slavin produces at the level found in requirement (a), how much will monthly profit increase over the current production schedule?