Duke Co. has many years of history as a manufacturer of antique, hand made furniture. Style has been recently known for its three luxurious chairs: Richard1, Richard2 and Richard3 manufactured in its three production departments: Carpentry, Grindery and Varnish. Unfortunately demand for all the products exceeds the company's ability to meet the customers' needs. The selling prices and the standard costs of each product are given below. Specification Richard1 Richard2 Richard3 Selling price (PLN per unit) 1210 1360 1520 Direct material cost (PLN per unit) 546 603 698 Direct labour (PLN per unit) -Carpentertary departament 160 192 208 Grindery departament 104 117 130 - Varnish Department 56 70 112 Variable over head (PLN per unit 44 81 68 1063 1216 The company has full-time labour workers available 8 hours per day, 6 days per week and 4 weeks per month and this workforce can be supplemented by part-time workers who are employed as and when required. This additional information is shown below. Both full-time workers and part-time workers are paid the same labour hour rate. FErt-Line WOIRTorCE available (hours per Deprtament Number of full-time worker [month Hour rate (PLN per hour) Carpentery 16 1048 8 Grindery 9 432 6,5 CVarnish 12 776 Raw materials required in the production process are sufficient and continuously available to manufacture any planned quantity of all antique chairs. Duke's monthly fixed costs amount to 4 000 PLN. Required: (a) Calculate the quantity of chairs (Richard1, Richard2 and Richard3) available to manufacture in each department. (4 marks) (b) Find a limiting factor, determine the ranking of the chairs according to which of them should be produced in order to maximize the monthly operating income in the company and identify the optimal production programme, i.e. what quantities of the products should be manufactured in respect of the operating income. (8 marks) (c) Prepare a brief statement showing the maximized operating income. (3 mark) (d) Discuss the bottleneck and suggest how this could be solved