Exam 21: Linear Programming Using the Excel Solver

Formulate and solve the following linear program.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 is $87.Although the firm can readily sell any amount of either product,it is limited by its total labor hours and total machine hours available.The total labor hours per week are 4,000.Product D takes 5 hours of labor per unit and product E takes 7 hours of labor per unit.The total machine hours are 5,000 per week.Product D takes 9 hours of machine time per unit and product E takes 3 hours of machine time per unit.Write the constraints and the objective function for this problem,solve for the best mix of product D and E and report the maximum value of the objective function?

Apply linear programming to this problem.David and Harry operate a discount jewelry store.They want to determine the best mix of customers to serve each day.There are two types of customers for their store,retail (R)and wholesale (W).The cost to serve a retail customer is $70 and the cost to serve a wholesale customer is $89.The average profit from either kind of customer is the same.To meet headquarters' expectations,they must serve at least 8 retail customers and 12 wholesale customers daily.In addition,in order to cover their salaries,they must at least serve 30 customers each day.Which of the following is one of the constraints for this model?

Each term in a linear program's objective function should be expressed in the same units.

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 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?

Which of the following is an essential condition in a situation for linear programming to be useful?

In the formulation of a linear programming model we expect to see a requirement on all the decision variables to be either zero or some positive value.

What is the shadow price of a non-binding constraint? Why is this so?

Apply linear programming to this problem.A one-airplane airline wants to determine the best mix of passengers to serve each day.Their airplane seats 25 people and flies 8 one-way segments per day.There are two types of passengers: first class (F)and coach (C).The cost to serve each first class passenger is $15 per segment and the cost to serve each coach passenger is $10 per segment.The marketing objectives of the airplane owner are to carry at least 13 first class passenger-segments and 67 coach passenger-segments each day.In addition,in order to break even,they must at least carry a minimum of 110 total passenger segments each day.Which of the following is one of the constraints for this linear program?

Finding the optimal location of a new plant by evaluating shipping costs between alternative locations and supply and demand sources is one kind of problem that can be solved by linear programming.

There are other related mathematical programming techniques that can be used instead of linear programming if the problem has a unique characteristic.If the problem has multiple objectives we should use which of the following methodologies?

Finding the optimal routing for a product that must be processed sequentially through several machine centers,with each machine in a center having its own cost and output characteristics cannot be solved using linear programming.

If products and resources can not be subdivided into fractions,the condition of divisibility is violated.In these cases,a modification of linear programming called integer programming can be used.

There are other related mathematical programming techniques that can be used instead of linear programming if the problem has a unique characteristic.If the problem is best solved in stages or time frames we should use which of the following methodologies?

The number of decision variables allowed in a linear program is which of the following?

Which of the following is not an essential condition in a situation for linear programming to be useful?

Finding the optimal combination of products to stock in a retail store cannot be solved using linear programming.

Linear programming is gaining wide acceptance in many industries due to the availability of detailed operating information and the interest in optimizing processes to reduce cost.

Linear programming is useless when resources are plentiful relative to demand.

The number of constraints allowed in a linear program is which of the following?

The decision variables in a linear programming model must be non-negative.