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Falditas Inc. is a company that is specialized in producing very high-end skirts. Currently, the company produces long and short skirts. Each type of skirt requires a certain amount of processing time distributed as follows:
For producing one long skirt, Falditas needs 6 yards of raw materials. This quantity is smaller (4 yards) when it comes to short skirts. These products have very high quality and their price reflects that: after taking costs into consideration, the marginal profits are $190 and $150 for long skirts and short skirts, respectively.
Falditas Inc. have to decide on their production quantities for next week as to maximize their profit. They have 1200 yards of fabric available. They also have 200 hours for cutting and 180 for sewing. However, if needed, they can schedule overtime for these two processes, at a cost of $15/hour of cutting time and $10/hour of sewing time. They cannot schedule overtime indefinitely, so they have a limit of 100 hours of overtime.
The company wants to produce a minimum of 100 long skirts and 75 shorts skirts next week. Let L and S be the number of long and short skirts produced, respectively and O_{c}, O_{s} be the number of hours of overtime or cutting and sewing respectively. The use an LP model to maximize profits, which they solve in Excel. The computer solution is shown below:
Optimal profit: $ 40,900
Variable Cells | |||||||
Final | Reduced | Objective | Allowable | Allowable | |||
Cell | Name | Value | Cost | Coefficient | Increase | Decrease | |
$C$9 | L (units) | 100 | 0 | 190 | 35 | Inf | |
$D$9 | S (units) | 150 | 0 | 150 | Inf | 23.33 | |
$E$9 | Oc (hours) | 40 | 0 | -15 | 15 | 172.5 | |
$F$9 | Os (hours) | 0 | -10 | -10 | 10 | Inf | |
Constraints | |||||||
Final | Shadow | Constraint | Allowable | Allowable | |||
Cell | Name | Value | Price | R.H. Side | Increase | Decrease | |
$B$15 | Cutting LHS | 200 | 15 | 200 | 40 | 60 | |
$B$16 | Sewing LHS | 160 | 0 | 180 | Inf | 20 | |
$B$17 | Overtime limit LHS | 40 | 0 | 100 | Inf | 60 | |
$B$18 | Material limit LHS | 1200 | 34.5 | 1200 | 133.33 | 200 | |
$B$19 | Production limit L LHS | 100 | -35 | 100 | 50 | 100 | |
$B$20 | Production limit S LHS | 150 | 0 | 75 | 75 | Inf |
A medical facility operates between 11 am and 10 pm. Their staff is made of part-time employees who work in shifts of four hours (i.e. an employee that starts at noon will finish at 4 pm). On average, the wage for these employees is $7.60 per hour. In view of the number of patients that this facility usually has to serve, management considers that they will need the following employees: 8 employees between 11 am and noon; 8 employees between noon and 1 pm; 7 employees between 1 pm and 2 pm; 1 employee between 2 pm and 3 pm; 2 employees between 3 pm and 4 pm; 1 employee between 4 pm and 5 pm; 5 employees between 5 pm and 6 pm; 10 employees between 6 pm and 7 pm; 10 employees between 7 pm and 8 pm; 6 employees between 8 pm and 9 pm; and 6 employees between 9 pm and 10 pm.
Management is asking you to come up with a schedule for part time-employees (i.e. they want to know how many employees should start shifts and 11 am, noon, 1 pm, etc.) such that the total cost in wages is minimized.