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A company manufactures two models of voltage stabilizers viz., ordinary and auto-cut. All components of the stabilizers are purchased from outside sources, assembly and testing is carried out at the - Business Mathematics and Statistics

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प्रश्न

A company manufactures two models of voltage stabilizers viz., ordinary and auto-cut. All components of the stabilizers are purchased from outside sources, assembly and testing is carried out at the company’s own works. The assembly and testing time required for the two models are 0.8 hours each for ordinary and 1.20 hours each for auto-cut. Manufacturing capacity 720 hours at present is available per week. The market for the two models has been surveyed which suggests a maximum weekly sale of 600 units of ordinary and 400 units of auto-cut. Profit per unit for ordinary and auto-cut models has been estimated at ₹ 100 and ₹ 150 respectively. Formulate the linear programming problem.

योग
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उत्तर

(i) Variables: Let x1 and x2 denote the number of ordinary and auto-cut voltage stabilized.

(ii) Objective function:

Profit on x1 units of ordinary stabilizers = 100x1

Profit on x2 units of auto-cut stabilized = 150x2

Total profit = 100x1 + 150x2

Let Z = 100x1 + 150x2, which is the objective function.

Since the profit is to be maximized. We have to Maximize, Z = 100x1 + 15x2

(iii) Constraints: The assembling and testing time required for x1 units of ordinary stabilizers = 0.8x1 and for x2 units of auto-cut stabilizers = 1.2x2

Since the manufacturing capacity is 720 hours per week.

We get 0.8x1 + 1.2x2 ≤ 720

Maximum weekly sale of ordinary stabilizer is 600 i.e., x1 ≤ 600

Maximum weekly sales of auto-cut stabilizer is 400 i.e., x2 ≤ 400

(iv) Non-negative restrictions: Since the number of both the types of stabilizers is non-negative, we get x1, x2 ≥ 0.

Thus, the mathematical formulation of the LPP is, Maximize Z = 100x2 + 150x2

Subject to the constraints

0.8x1 + 1.2x2 ≤ 720, x1 ≤ 600, x2 ≤ 400, x1, x2 ≥ 0

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अध्याय 10: Operations Research - Exercise 10.1 [पृष्ठ २४४]

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सामाचीर कलवी Business Mathematics and Statistics [English] Class 11 TN Board
अध्याय 10 Operations Research
Exercise 10.1 | Q 3 | पृष्ठ २४४

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