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 $100andtheprofitinthemanufactureofaunitofproductEis$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?

• A. $5D+7E\le 5,000$
• B. $9D+3E\ge 4,000$
• C. $5D+7E=4,000$
• D. $5D+9E\le 5,000$
• E. $9D+3E\le 5,000$

Answer 1

The correct option is E $9D+3E\le 5,000$

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 and

to produce E units of product E takes $7E$ hours

Given, total labour hours per week are $4000$ hours.

Hence, $5D+7E\le 4000$

Given, product D takes 9 hours per unit of machine time, and

product E takes 3 hours per unit of machine time.

Therefore, to produce D units of product D takes $9D$ hours and

to produce E units of product E takes $3E$ hours

Given, total machine hours per week are $5000$ hours.

Hence, $9D+3E\le 5000$