SOLUTION: Healthy Foods has brought out a new breakfast cereal called Hi-Fibre, which uses a concentrated form of fibre developed by their own research laboratory. This product has been tes

Question 1057819: Healthy Foods has brought out a new breakfast cereal called Hi-Fibre, which uses a concentrated form of fibre developed by their own research laboratory. This product has been test marketed in a few selected areas and the consumer reaction has been favourable. However several people questioned said they would prefer a higher fibre content, so George Brown, the Product manager has decided to meet this demand with an additional product called Hi-Fibre Plus. This product will double the fibre content of Hi-Fibre and also require extra cooking time. The selling price of Hi-Fibre Plus will be greater than that for Hi-Fibre and so will the contribution to profits. For Hi-Fibre the contribution will be 12p per 500g packet, for Hi-Fibre Plus it will be 15p per 500g packet.
During the period of test marketing, 500 packets were produced each day but from a commercial point of view at least 2500 packets of each type must be produced and it is expected that demand will soon exceed this figure. The storage area can take a maximum of 12000 packets so daily production cannot exceed this figure. There is one oven and one packaging plant that operates for 12 hours a day and the supply of concentrated fibre is, for the moment, limited to 120kg per day. George wants guidance on the number of each product to produce. The following information is also supplied.
Hi-Fibre Hi-Fibre Plus
Cooking/packaging 3 seconds 5 seconds
Fibre Content 5g 10g
Task One
Produce a graphical linear programming model to solve the problem and to present the possible solutions, indicating which one will give the greatest profit.
[50]
Task Two
Answer the following to give further insight into the situation:
a) How much of each resource (fibre, storage space and time) are left after optimal quantities of the cereal are produced. Which resources are scarce (i.e. used up)?
[10]
b) Is it worthwhile increasing the scarce resources and by how much? The additional cost of increasing fibre production is �20 per kg, storage space would work out at 20p per packet and extending the working day would incur costs of �30 per hour.
[10]
c) Would the optimal solution change if the profit contribution changed?
[15]
d) The sales department believes that demand for Hi-Fibre Plus will be greater than demand for Hi-Fibre. If this is correct then production of Hi-Fibre Plus needs to be higher than Hi-Fibre. What increase in profit contribution will be necessary if the total profit is to remain the same?
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.
School math problem?

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