A garden store prepares various grades of wood chips for mulchfor sale in various tonnages for delivery to large gardenconstruction sites around town. The grades are (a) fine, (b)standard and (c) course. The process requires red gum, machinetime, labour time, and storage space.
The garden store owner has identified that the store cangenerate $90 profit per storage bin for fine, $90 for standard butonly $60 for course chips.
Each load of chips require inputs in the followingquantities:
Fine: 5 tonnes of material, 2 machine hours, 2 hours of labour and1 storage bin Standard: 6 tonnes of material, 4 machine hours, 4hours of labour and 1 storage bin Course: 3 tonnes of material, 5machine hours, 3 hours of labour and 1 storage bin
Unfortunately, like every business, the garden store has limitsin its production capacity. It is able to handle 600 tonnes of redgum at any one time, the machine can only operate for 600 hoursbefore major maintenance must occur, it only has sufficient staffto provide 480 hours of labour time and it has 150 storagebins.
Required:
please give all calculations
(a) What is the marginal value of a tonne of red gum? Over whatrange is this price value appropriate?
(b) What is the maximum price the store would be justified inpaying for additional red gum?
(c) What is the marginal value of labour? Over what range isthis value in effect?
(d) The manager obtained additional machine time through betterscheduling. How much additional machine time can be effectivelyused for this operation? Why?
(e) If the manager can obtain either additional red gum oradditional storage space, which one should the manager choose andhow much (assuming additional
quantities cost the same as usual)?
(f) If a change in the course chip operation increased theprofit on course chips from $60 per bin to $70 per bin, would theoptimal quantities change? Would the value of the objectivefunction change? If so, what would the new value(s) be?
(g) If profits on course chips increased to $70 per bin andprofits on fine chips decreased by $6.00, would the optimalquantities change? Would the value of the objective functionchange? If so, what would the new value(s) be?
