Question

Royal Glass Inc. produces window glass and is making a special type of glass with a sun filter using new and recycled glass as raw materials. The company produces the glass in batches of 500 pieces and the budgeted sale for the current year is 6.000 pieces of glass. The company produces the glass in various combinations of new and recycled glass. Royal Glass can buy new glass for a price per kilo of 250.00 DKK and recycled glass for a price per kilo of 149.00 DKK. Royal Glass receives a discount on 10% on purchasing of new glass on orders with a minimum of 10,000 kg new glass (no discount on recycled glass). All purchased glass, new as well as recycled is used for production in order not to have raw materials on inventory. Though, in case of inventory of finished glass (not raw materials) the financial department has estimated the cost of inventory to be 12% of the inventory value. The possible combinations of new and recycled glass used for producing one piece of glass with sun-filter are as follows: Recycled glass (kg) 6.5 6.15 5.75 5.65 5.4 5.1 4.5 4.1 3.8 4.0 New glass (kg) 1.1 1.25 1.5 1.6 1.8 2.0 2.3 2.8 3.4 4.8 Required A. Calculate the optimal combination of new and recycled glass to minimize average production cost per piece of glass with sun-filter? B. Should the manager use the option of 10% discount for ordering more than 10,000 kg new glass? Explain your answer. C. All Royal Glass's overhead cost is allocated to the production department based on the amount of recycled glass used in the production. One kilo (kg) of recycled glass is charged with 30.00 DKK. Does this cost change the optimal combination of new and recycled glass?

Answer 1

A. Calculation of Glass Inc optimal production cost
Recycled glass(Kg)	No. of pieces required	Per piece cost	New glass	No. of pieces required
	for 6000 sales			for 6000 sales	Per piece cost	Total cost
6.5	39000	968.5	1.1	6600	275	1243.5
6.15	36900	916.35	1.25	7500	313	1228.85
5.75	34500	856.75	1.5	9000	375	1231.75
5.65	33900	841.85	1.6	9600	400	1241.85
5.4	32400	804.6	1.8	10800	405	1209.6
5.1	30600	759.9	2	12000	450	1209.9
4.5	27000	670.5	2.3	13800	518	1188
4.1	24600	610.9	2.8	16800	630	1240.9
3.8	22800	566.2	3.4	20400	765	1331.2
4	24000	596	4.8	28800	1080	1676
The optimal combination is use 4.5 kg Recycled glass and 2.3 new glass.
B. No pieces sold for the year- 6000 pieces
Required raw materials at optimal cost
for l piece of glass
				No. of pieces required for 6000 pieces of production
Recycled glass			4.5 Kg	27000
New glass			2.3 Kg	13800
At the optmal cost the new glass of inventory we need is more than 10000 kgs. So we can use the option of 10% discount.
Recycled glass(Kg)	No. of pieces required	Per piece cost	New glass	No. of pieces required
	for 6000 sales			for 6000 sales	Per piece cost	Overhead cost	Total cost
6.5	39000	968.5	1.1	6600	275	195	1438.5
6.15	36900	916.35	1.25	7500	313	184.5	1413.35
5.75	34500	856.75	1.5	9000	375	172.5	1404.25
5.65	33900	841.85	1.6	9600	400	169.5	1411.35
5.4	32400	804.6	1.8	10800	405	162	1371.6
5.1	30600	759.9	2	12000	450	153	1362.9
4.5	27000	670.5	2.3	13800	518	135	1323
4.1	24600	610.9	2.8	16800	630	123	1363.9
3.8	22800	566.2	3.4	20400	765	114	1445.2
4	24000	596	4.8	28800	1080	120	1796
Even overhead cost is calculated the optimal combination of 4.5 kg recycled glass and 2.3 kg of new glass is not