A niche rum manufacturer wants to determine their weekly production plan. They p
ID: 345143 • Letter: A
Question
A niche rum manufacturer wants to determine their weekly production plan. They produce rums in three sizes. They prepare the bottles (clean /label them) and then bottle/seal them (therefore 2 main steps). Production of the rum is limited to 1,000L per week. There is a total of 200 hours available for preparing bottles and 80 hours available for bottling/ sealing. To meet a standing order, the plan must include at least 50 units of the 1.5L size. A maximum of 30% of the production (in terms of units) can be of the 0.33L size.
Bottle size
Time to prepare bottle
Time to bottle/seal
Profit/bottle
1.5L
5 min
2.5 min
$4
0.75L
4 min
1.6 min
$2.3
0.33L
3.2 min
1.2 min
$1.1
Bottle size
Time to prepare bottle
Time to bottle/seal
Profit/bottle
1.5L
5 min
2.5 min
$4
0.75L
4 min
1.6 min
$2.3
0.33L
3.2 min
1.2 min
$1.1
Explanation / Answer
This can modelled as linear programming problem.
Let X1 be the number of the units of 1.5L bottles produced, let X2 be the number of units of 0.75L produced and X3 be the number of units of 0.33L bottles produced.
The objective is to maximize profit
Maximize Z = $ 4X1 + $ 2.3X2 + $ 1.1X3
subject to the following constraints
X1 + X2 + X3 less than equal to 1000
5X1 + 4X2 + 3.2 X3 less than or equal to 200 hrs
2.5X1 + 1.6X2 + 1.2X3 less than or equal to 80 hours
X1 greater than equal 50
X3 less than equal to 300
Solving using microsoft excel solver. As per solver we should produce 32 units of 1.5L rum to maximize the profits.
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