Par Inc

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```					                                        Par Inc.

Par Inc. manufactures two types of golf bags: Standard and Deluxe. Profit for the Standard bag is \$9 and
profit for the Deluxe bag is \$15. Each bag must go through the four departments shown below. The table
also shows the number of hours it takes to process a bag for each department and the maximum hours each
department can work per month.

Assuming an unlimited demand, how many bags of each type should Par Inc. produce per month to maximize
profit?

Cutting                            Inspection &
and Dying        Sewing Finishing      Packaging
Standard Bag Hours Per Dept:     0.70           0.50     1.00            0.10
Deluxe Bag Hours Per Dept:     2.00           0.83     0.67            0.25
Max Hours Per Dept Per Month:   630.00         600.00  708.00          135.00
o maximize
Inspection
Cutting                                 &
and Dying   Sewing   Finishing   Packaging
Standard Bag Hours Per Dept:     0.70      0.50       1.00         0.10
Deluxe Bag Hours Per Dept:     2.00      0.83       0.67         0.25
Max Hours Per Dept Per Month:   630.00    600.00    708.00        135.00

Standard Bags:
Deluxe Bags:
Grand Total
Par Inc.

Par Inc. manufactures two types of golf bags: Standard and Deluxe. Profit for the Standard bag is \$9 and
profit for the Deluxe bag is \$15. Each bag must go through the four departments shown below. The table
also shows the number of hours it takes to process a bag for each department and the maximum hours each
department can work per month.

Assuming an unlimited demand, how many bags of each type should Par Inc. produce per month to maximize
profit?

Cutting                                   Inspection &
and Dying             Sewing Finishing        Packaging
Standard Bag Hours Per Dept:     0.70                0.50     1.00              0.10
Deluxe Bag Hours Per Dept:     2.00                0.83     0.67              0.25
Max Hours Per Dept Per Month:   630.00              600.00  708.00            135.00

Solution
Profit for Standard Bag is: \$      9.00
Profit for Deluxe Bag is: \$     15.00

Total Profit is:
(Number of Stardard bags * \$9) + (Number of Deluxe bags * \$15)

However, because of time constraints, each department can only produce a limited number of bags per
month. Therefore, total bags is limited by the department which reaches its maximum production hours for
a particular type of bag first.

The equation to find the total hours per department per month is:
(Number of Deluxe Bags * Hrs. Per Deluxe bag) + (Number of Std. Bags * Hrs. Per Std. bag)

1. Dept Hrs. Per Month:
For each dept. and both types of bags, multiply the number of bags (guess for now) by the hours it takes
to produce the bag type.

3. Multiply Total Number of each type per of bag
2. Number of Bags Per Month:                                       produced per month by the profit per bag.
Guess for now.
Cutting &                           Inspection &
Number       Dying     Sewing       Finishing   Packaging
of Bags    Hrs. Per   Hrs. Per       Hrs. Per     Hrs. Per   Profit Per
Per Mon.      Month      Month          Mohth        Month       Month
Standard:              10          7.0        5.0          10.0           1.0 \$    90.00
Deluxe:              10        20.0         8.3            6.7          2.5 \$ 150.00
Monthly Totals:             20        27.0       13.3           16.7           3.5
Max Hours Per Month:                         630        600            708          135
Total Profit:                                                                   \$ 240.00

Monthly Totals:                                                                         4. Total Profit: Sum the
5. Sum the Number of Standard Bags & Deluxe Bags.                                       profit for Standard &
6. Sum the Number of Standard Hours & Deluxe hours for each department.                 Deluxe bags.

Now that the Equations have been set up you are now ready to use Solver:

Goal:
Goal:
To Maximize Total Profit by altering the total number of Standard & Deluxe bags we are producing.

Constraints:
Total Cutting & Dying Hrs. Per Month <= 630
Total Sewing Hrs. Per Month <=600
Total Finishing Hrs. Per Month <=708
Total Inspection & Packaging Hrs. Per Month <=135

If we made JUST Standard or JUST Deluxe
Cutting                          Inspection &    Max Bags
and Dying        Sewing Finishing     Packaging     Per Month Total Profit
900
Max # Bags Standard per Month per Dept.:           1200      708           1350          708 \$ 6,372.00
Max # Bags Deluxe per Month per Dept.: 315          720     1062             540         315 \$ 4,725.00
aximize

pe per of bag

Sum the
Inspection
Cutting &                                   &
Number     Dying     Sewing    Finishing   Packaging
of Bags Hrs. Per    Hrs. Per    Hrs. Per     Hrs. Per   Profit Per
Per Mon.   Month       Month       Mohth        Month       Month
Standard:         650   454.70     324.78      649.57         64.96 \$ 5,846.09
Deluxe:          88   175.30       73.04       58.43        21.91 \$ 1,314.78
Monthly Totals:        737    630.0       397.8       708.0         86.9
Max Hours Per Month:                   630        600         708          135
Total Profit:                                                          \$ 7,160.87
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