| Information about the products, relating to the foreseeable future, is as follows: | A | B | C |
| Material X usage (metres per product) | 55 | 25 | 20 |
| Manufacturing labour (minutes per product) | 40 | 35 | 50 |
| Selling price ($ per product) | 20.00 | 16.00 | 20.00 |
| Other materials ($ per product) | 1.50 | 1.00 | 1.00 |
| Expected demand (Units per week) | 200 | 500 | 200 |
Material X costs the business $0.10 a metre and the manufacturing workers are paid
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$8 an hour. The manufacturing workers are all employed on contracts that guarantee all 12 of them a 40-hour week (that is, the manufacturing workers are paid $320 a week, irrespective of the amount of work carried out). There are no other employment costs associated with the workers.
It is not possible to expand the staff by employing other manufacturing workers and the existing ones are reluctant to work overtime.
Material X is in short supply and only 30,000 metres a week are expected to be available for the foreseeable future. The business holds no inventories of Material X. Supplies of it are received at the beginning of each week.
The business incurs manufacturing overheads that are believed to be partially fixed and partially variable with manufacturing labour time. During two recent consecutive weeks, this cost totalled $2,700 in Week 1 and $3,010 in Week 2.
| Output for those two weeks was as follows: Week | A | B | C |
| 1 | 150 | 320 | 160 |
| 2 | 150 | 380 | 180 |
There have not been, nor are there expected to be in the foreseeable future, any price changes, either of sales prices or of cost elements.
Required:
(1) Prepare calculations that indicate whether it is the current level of staffing or the supply of Material X that will constrain the business from meeting the expected demand for the products.
(2) Determine, with clear workings and justification (including assumptions made), the optimal quantity of each product that the business should produce each week.
(3) Determine:
(a) the maximum amount that the business should be prepared to pay as an overtime rate to the manufacturing workers, should any of them be prepared to work extra hours; and
(b) the maximum amount that the business should be prepared to pay for any additional quantities of Material X.
In each case explain how any additional resources would be deployed, if at all.
(4) Explain what steps the business might take to improve its profitability in the near future.
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