Intermediate: Limiting factor optimum production and the use of simultaneous equations where more than one scarce factor exists A company manufactures two products (X and Y) in one of its factories. Production capacity is limited to 85 000 machine hours per period. There is no restriction on direct labour hours.

The following information is provided concern¬ ing the two products:

Fixed costs are absorbed into unit costs at a rate per machine hour based upon full capacity.
Required:

(a) Calculate the production quantities of Products X and Y which are required per period in order to maximize profit in the situation described above. (5 marks)

(b) Prepare a marginal costing statement in order to establish the total contribution of each product, and the net profit per period, based on selling the quantities calculated in

(a) above. (4 marks)

(c) Calculate the production quantities of Products X and Y per period which would fully utilize both machine capacity and direct labour hours, where the available direct labour hours are restricted to 55 000 per period. (The limit of 85 000 machine hours remains.)

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Product Product X Y Estimated demand (000 units) 315 135 Selling price (per unit) 11.20 15.70 Variable costs (per unit) 6.30 8.70 Fixed costs (per unit) 4.00 7.00 Machine hours (per 000 units) 160 280 Direct labour hours (per 000 units) 120 140