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Fruity Co manufactures two types of concentrated fruit juice; Kee and Max for domestic and oversea markets. Both are made purely from fresh apples that are bought from a family-owned apple farm operator. The production of Kee and Max shared the same production facilities where the machines in used are semi-manually operated.
The standard cost and selling price information of both the products are given below:
Per litre of concentrated fruit juice
Kee$
Max
$
Apple ($10 per kilogram) 20.00 10.00
Machine ($15 per machine hour) 15.00 37.50
Labour ($12 per labour hour) 9.60 12.00
Other variable overheads 9.40 8.50
Total variable costs 54.00 68.00
Selling price 58.00 74.00
Fixed costs per month is agreed at $7,000.
To ensure a smooth and uninterrupted production operation, Fruity Co will always need to monitor closely on all the possible constraints in every upcoming month in determining the optimum production plan in order to maximise its return with the given constraints.
In the midst of the planning process for following month, Fruity Co has agreed to supply at least 2,500 litres of Kee to one of the oversea customers and the agreement has signed recently. Given the routine machine maintenance and normal staffing arrangement, the maximum available machine hours and labour hours for the following month are expected to cap at 25,000 hours and 15,000 hours respectively. The apple farm operator has informed Fruity Co that the supply of apple will be kept at a quota of 24,000 kilograms.
Based on the above constraints, it had formulated and graphed with the unknown ‘k’ being the output (litres) of Kee and unknown ‘m’ being the output (litres) of Max as below:
C1. Apple: 2k + m ? 24,000
C2. Machine: k + 2.5m ? 25,000
C3. Labour: 0.8k + m ? 15,000
C4. Minimum order: k ? 2,500
Non-negativity: k, m ? 0
what is the optimum production plan and shadow price of materials
this question is from pre june 2024 mock