
Concept explainers
Explanation of Solution
Finding optimal solution:
The demand for sail boats during each of the next four quarters is;
First quarter-40 sailboats
Second quarter-60 sailboats
Third quarter- 75 sailboats
Fourth quarter- 25 sailboats
An inventory of 10 sailboats is at the beginning of the first quarter. Also, it is assumed that sailboats manufactured during a quarter can be used to meet demand for that quarter.
Also, during each quarter, Sailco can produce up to 40 sailboats with total cost of $400 per sailboat.
Additional sailboats with overtime labor can be produced at a total cost of $450 per sailboat.
A carrying cost of $20 per sailboat is incurred at the end of each quarter. A production schedule to minimize the sum of production and inventory costs during the next four quarters using linear
Let,
Sailco’s total cost can be determined as follows.
Since the total cost to be minimized, the objective function of Sailco is given below,
Minimize,
The constraints are given below,
For each period’s regular time production will not exceed 40. So the below given constraints are obtained.
Also suppose that,
This means,
When submitting the values, the following constraints are obtained.
Also,

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Chapter 4 Solutions
Introduction to mathematical programming
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