A company makes three products A, B and C, which all require two types of machine: cutting machines and assembling machines. Estimates for next year include the following:

Product A:
Selling price (per unit): $25
Sales demand (units): 2,500
Direct material cost (per unit): $12
Variable production cost (per unit): $7
Time required per unit on cutting machines: 1 hours
Time required per unit on assembling machines: 0.5 hours
Product B:
Selling price (per unit): $30
Sales demand (units): 3,400
Direct material cost (per unit): $13
Variable production cost (per unit): $4
Time required per unit on cutting machines: 1 hours
Time required per unit on assembling machines: 1 hours
Product C:
Selling price (per unit): $18
Sales demand (units): 5,100
Direct material cost (per unit): $10
Variable production cost (per unit): $3
Time required per unit on cutting machines: 0.5 hours
Time required per unit on assembling machines: 0.5 hours

Fixed overhead costs for next year are expected to total $42,000. It is the company's policy for each unit of production to absorb these in proportion to its total variable costs. The company has cutting machine capacity of 5,000 hours per annum and assembling machine capacity of 8,000 hours per annum.

a) From this information, determine (with supporting workings) which products in which quantities the company should plan to make next year.
b) State the maximum price per product that would make it worth paying a subcontractor to carry out that part of the work the company could not do internally.