3. Vollmer Manufacturing makes three components for sale to refrigeration companies. The components are processed on two machines: a sharper and a grinder. The times (in minutes) required on each machine are as follows:

Machine

Component Sharper Grinder

1 6 4

2 4 5

3 4 2

The sharper is available for 120 hours, and the grinder is available for 110 hours. No more than 200 units of component 3 can be sold, but up to 1000 units of each other components can be sold. In fact, the company already has orders for 600 units of component 1 that must be satisfied. The profit contributions for components 1, 2, and 3 are $8, $6, and $9, respectively.

a. Formulate this LP problem and make sure you define all the decision variables.

b. Transform your formulation to the Standard LP form.

c. The Excel Solver Solution to this problem is presented below. Identify and present the optimal solution and the values of the decision variables.

d. Find the slack and/or surplus variables.

e. Will the Sharper or the Grinder or both need more time? Explain.

f. Identify the ranges of optimality and the ranges of feasibility. Discuss them in relation to this problem. Hint: Do not give a general discussion on this question. You must be very specific and use all the results you now have.

Microsoft Excel Report

Objective function $10800

Variable Cells

Final Reduced Objective Allowable Allowable

Cell Name Value Cost Coefficient Increase Decrease

$C$19 Component 1 600 0 8 1 1E+30

$D$19 Component 2 700 0 6 3 0.666667

$E$19 Component 3 200 0 9 1E+30 3

Constraints

Final Shadow Constraint Allowable Allowable

Cell Name Value Price R.H. Side Increase Decrease

$C$23 Sharper LHS 7200 1.5 7200 240 2800

$C$24 Grinder LHS 6300 0 6600 1E+30 300

$C$25 Component 1 LHS 600 -1 600 400 85.71429

$C$26 Component 1 LHS 600 0 1000 1E+30 400

$C$27 Component 2 LHS 700 0 1000 1E+30 300

$C$28 Component 3 LHS 200 3 200 700 100