please answer the question below:

1-

A business makes three products, X, Y and Z. Each of the products requires the use of labour and of materials, including a special material, Material A. Manufacturing labour is equally capable of working on all three products.

Demand for all three products has increased strongly over recent months and is expected to remain high.

Information about the products, relating to the foreseeable future, is as follows:

X Y Z

Material A usage (metres per product) 55 25 20

Manufacturing labour (minutes per product) 40 35 50

Selling price ($ per product) 20 16 20

Other materials ($ per product) 1.50 1.00 1.00

Expected demand (units a week) 200 500 200

Manufacturing overheads ($ per product) 4.0 3.50 5.00

Material A costs the business $0.10 a meter and the manufacturing workers are paid $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.

For Material A, 30,000 meters a week are expected to be available for the foreseeable future. The business holds no inventories of Material A. Supplies of it are received at the beginning of each week.

No changes are expected, in the foreseeable future, regarding sales price and cost elements.

Required

1. Prepare calculations that indicate whether it is the current level of staffing or the supply of Material A that will constrain the business from meeting the expected demand for all three products.
2. Determine, with clear workings and justification, the optimal quantity of each product that the business should produce each week.
3. Determine:

• 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.
• The maximum amount that the business should be prepared to pay for any additional quantities of Material A.

In each case explain how any additional resources would be deployed, if at all.

Explain what steps the business might take to improve its profitability in the near future.