Utilization of Constrained Resources – WuHan Paint Company

WuHan Paint Company makes three products in a single facility. These products have the following unit product costs:

Products
A / B / C
Direct materials / ¥22.50 / ¥22.40 / ¥29.20
Direct labor / 13.60 / 11.40 / 12.50
Variable manufacturing overhead / 3.00 / 3.40 / 4.50
Fixed manufacturing overhead / 19.20 / 20.10 / 26.50
Unit product cost / ¥58.30 / ¥57.30 / ¥72.70

Additional data concerning these products are listed below.

Products
A / B / C
Mixing minutes per unit / 3.30 / 1.70 / 1.80
Selling price per unit / ¥74.70 / ¥76.10 / ¥87.50
Variable selling cost per unit / ¥1.80 / ¥2.40 / ¥2.90
Monthly demand in units / 4,000 / 2,000 / 4,000

The mixing machines are potentially the constraint in the production facility. A total of 23,200 minutes are available per month on these machines.

Direct labor is a variable cost in this company.

Required:

a.  How many minutes of mixing machine time would be required to satisfy demand for all three products?

b.  How much of each product should be produced to maximize net operating income? (Round off to the nearest whole unit.)

c.  Up to how much should the company be willing to pay for one additional hour of mixing machine time if the company has made the best use of the existing mixing machine capacity? (Round off to the nearest whole RMB.)

ANSWER:

Short Case Utilization of Constrained Resources – WuHan Paint Company

a.  Demand on the mixing machine:

Product
A / B / C
Mixing minutes per unit / 3.30 / 1.70 / 1.80
Monthly demand in units / 4,000 / 2,000 / 4,000
Total minutes required / 13,200 / 3,400 / 7,200

Total time required for all products: 23,800

b. / Optimal production plan:
Product
A / B / C
Selling price per unit / ¥74.70 / ¥76.10 / ¥87.50
Direct materials / ¥22.50 / ¥22.40 / ¥29.20
Direct labor / 13.60 / 11.40 / 12.50
Variable manufacturing overhead / 3.00 / 3.40 / 4.50
Variable selling cost per unit / 1.80 / 2.40 / 2.90
Total variable cost per unit / ¥40.90 / ¥39.60 / ¥49.10
Contribution margin per unit / ¥33.80 / ¥36.50 / ¥38.40
Mixing minutes per unit / 3.30 / 1.70 / 1.80
Contribution margin per minute / ¥10.24 / ¥21.47 / ¥21.33
Rank in terms of profitability / 3 / 1 / 2
Optimal production / 3,818 / 2,000 / 4,000

c.  The company should be willing to pay up to the contribution margin per minute for the marginal job, which is ¥10.24.