You own a coffee shop in a metro Toronto shopping mall. It is Friday evening and you are trying to decide how many dozen blueberry muffins to bake for the Saturday morning rush.
Based upon your experience with Saturdays, you think that the probability of being able to sell 5 dozen is 0.25, of being able to sell 10 dozen in 0.55, of being able to sell 15 dozen is 0.15 and of being able to sell 20 dozen is 0.05
A dozen muffins sells for $10.00 and has an incremental cost of $6.25. If you have leftover muffins, you will them to the local food bank for $2.25 each.
Use your knowledge of decision analysis to model and solve this problem in order to recommend the number of dozen muffins that should be baked.
Linear Programming Problem
A manufacturer of three models of tote bag must determine the production plan for the next quarter.
The specifics for each model are shown in the following table.
|
Model
|
Revenue ($ per item)
|
Cutting (hours per item)
|
Sewing (hours per item)
|
Packing (hours per item)
|
|
A
|
$8.75
|
.10
|
.05
|
.20
|
|
B
|
$10.50
|
.15
|
.12
|
.20
|
|
C
|
$11.50
|
.20
|
.18
|
.20
|
|
|
|
|
|
|
Time available in the three production departments are: Cutting 450 hours, Sewing 550 hours, Packing 450 hours.
Based on market research, the company wants to make at least 300 model A's, 400 model B's and 250 model C's but no more than no more than 1200 of any one model
Costs in each department are: Cutting $10.00 per hour, Sewing $12.50 per hour, Packing $9.50 per hour
Write the Linear Programming formulation for this problem to help determine the best production mix of the three models that will maximize profit.