QUESTION 1:
Springfield Paints produces both interior and exterior paints from two raw materials, m1 and m2. The following table provides the basic data for the problem:
Tons of raw material per ton of Maximum daily availability (tons)
Exterior paint Interior paint
Raw material m1 6 4 24
Raw material m2 1 2 6
Profit per tone ($1 000) 5 4
What is the number of tons of exterior and interior paint that have to be produced to maximize the profit? What is this profit? (You may evaluate your answers mathematically)
QUESTION 2:
A ready-mix concrete supplier delivers by truck to a dam site. Each truck is specified as containing 4800 + or – 50 kg. The supplier is concerned that his automatic concrete dispenser may not be capable of working to such a tight tolerance and that some trucks may contain less than the specified laod. The supplier has therefore been deliberately dispensing more than 4800 kg per truck.
A recently employed graduate is horrified by such apparent wastage and undertakes an investigation. As a first step, the graduate took a sample of five (5) trucks per day, over a fifteen day period and weighed their loads. The average load and range of each sample of the five trucks is given in the following table.
(i) Calculate the limits for the control charts you would use to assess the operation.
(ii) Plot the range chart and the average chart.
(iii) Find the relative precision index and calculate modified limits for the samples averages if warranted. If modified limits are not warranted, state why.
(iv) Determine whether the process is in, or out, of control and whether or not scrap is being produced. For the purpose of this question, any loads outside the upper or lower tolerances may be considered to be scrap.
(v) Advise the manager what action, if any, should be taken to improve the situation.
QUESTION 3:
The Luxuries Company makes canoe paddles to serve distribution centres in Warwick, Toowoomba and Ipswich from existing plants in Dalby and Kingsthrope. Luxuries is considering locating a plant near Oakey. Annual capacity in the plant is shown in the right-hand column, while annual demand is shown in the bottom row of the Table below. Transportation costs per paddle are shown in the small boxes. For example the cost to ship one paddle from Dalby to Warwick is $4.37.
Source Destination Capacity
Warwick Toowoomba Ipswich
Dalby $4.37 $4.25 $4.89 12 000
4 000 8 000
Kingsthorpe $4.00 $5.00 $5.27 10 000
2 000 4 000 4 000
Oakey $4.13 $4.50 $3.75 18 000
18 000
Demand 6 000 22 000 12 000 40 000
What is the optimum transportation plan to minimise delivery costs and what is the minimum total cost to Luxuries.
Please note you must find solutions via iterations and not just listing the final result from using a spreadsheet or software solution.