The XYZ Company manufactures two products, bidgets and badgets. The following data are available:

	Bidgets	Badgets
Selling price per unit	$60	$110
Variable cost per unit	$30	$70
Machine time per unit	30min	60min
Direct labour time per unit	40min	40min
Fixed costs	$5,000 per week
Available machine time	180 hours per week
Available direct labour time	220 hours per week

Required: (a) If direct labour time were the only scarce resource (i.e. there was an abundance of machine time) how many units of each product should be produced and sold each week in order to maximise profits? (5 marks)

(b) Given that both machine time and direct labour are limited as shown above, and that the manager wishes to produce three times as many badgets as bidgets, how many units of each product should be produced and sold to earn a weekly net profit of $2500? (8 marks)

(c) Build the LP Model and solve graphically. If both machine time and direct labour are limited as shown, how many units of each product should be produced and sold in order to maximise weekly net profits rather than produce a specified product mix as in (b)? What is the resulting net profit? (15 marks)

(d) The manager wishes to increase his factory capacity but is not sure whether to do so by working overtime or by leasing another machine. The overtime option would result in overtime wages payments of $5 per hour more than labour currently costs for regular hours. Alternatively, if another machine were leased no additional labour hours would be worked, but the leasing costs for the additional machine would be $10 per hour more than machine time leasing currently costs. (12 marks)

Advise the manager as to which alternative provides the higher increment to profit for each additional hour.