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Linear Programming — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsLinear Programming1 Mark
Question
Apply linear programming to this problem. A firm wants to determine how many units of each of two products (products D and E) they should produce to make the most money. The profit in the manufacture of a unit of product D is 100 and the profit in the manufacture of a unit of product E is100 and the profit in the manufacture of aunit of product E is 87. The firm is limited by its total available labor hours and total available machine hours. The total labor hours per week are 4,000. Product D takes 5 hours per unit of labor and product E takes 7 hours per unit. The total machine hours are 5,000 per week. Product D takes 9 hours per unit of machine time and product E takes 3 hours per unit. Which of the following is one of the constraints for this linear program?
  1. $5\text{D}+7\text{E}\leq5,000$
  2. $9\text{D}+3\text{E}\geq4,000$
  3. $5\text{D}+7\text{E}=4,000$
  4. $5\text{D}+9\text{E}\leq5,000$
  5. $9\text{D}+3\text{E}\leq5,000$
✓

Answer

  1. $9\text{D}+3\text{E}\leq5,000$

Solution:

Given, product D takes 5 hours per unit of labour, and product E takes 7 hours per unit of labour.

Therefore, to produce D units of product D takes 5D hours andto produce E units of product E takes 7E hours Given, total labour hours per week are 4000 hours.

Hence, $5\text{D}+7\text{E}\leq4,000$

Given, product D takes 9 hours per unit of machine time, andproduct E takes 3 hours per unit of machine time.

Therefore, to produce D units of product D takes 9D hours andto produce E units of product E takes 3E hours Given, total machine hours per week are 5000 hours.

Hence, $9\text{D}+3\text{E}\leq5,000$

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