Question

Formulate a system of equations for the situation below and solve.

A manufacturer of women's blouses makes three types of blouses: sleeveless, short-sleeve, and long-sleeve. The time (in minutes) required by each department to produce a dozen blouses of each type is shown in the following table.

The first column below is for sleeveless. The second is short sleeve. The third column is long sleeve.

Cutting 9 12 15

Sewing 22 24 28

Packaging 6 8 8

The cutting, sewing, and packaging departments have available a maximum of 79.5, 162, and 48 labor-hours, respectively, per day. How many dozens of each type of blouse can be produced each day if the plant is operated at full capacity?

Step 1

Let's assume a, b and c to be the number of dozens of sleeveless, short sleeve and long sleeve blouses produced per day resepctively.

Step 2

Number of minutes of cutting time required to support this production daily = 9a + 12b + 15c

Number of minutes of availability of cutting time = 79.5 hours x 60 minutes per hour = 4,770

Hence, 9a + 12b + 15c = 4,770 or, 3a + 4b + 5c = 1,590

Hence, Equation (1) is: 3a + 4b + 5c = 1,590

Step 3

Number of minutes of sewing time required to support this production daily = 22a + 24b + 28c

Number of minutes of availability of sewing time = 162 hours x 60 minu...

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