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. Sleeveless Short-Sleeve 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 78, 160, 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? sleeveless dozens short-sleeve dozens long-sleeve dozens Solve the following system of equations. 2x1 − x2 − x3 = −2 3x1 + 2x2 + x3 = 11 x1 + 2x2 + 2x3 = 9 (x1, x2, x3) =
Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
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.
Sleeveless | Short- Sleeve |
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 78, 160, 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?
2x1 | − | x2 | − | x3 | = | −2 |
3x1 | + | 2x2 | + | x3 | = | 11 |
x1 | + | 2x2 | + | 2x3 | = | 9 |
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