A company that makes concrete sells it in three quality levels, type 1 the being lowest, and
Question:
A company that makes concrete sells it in three quality levels, type 1 the being lowest, and type 3 being the highest. After deducting all variable costs, the net revenue is $30 per Tonne for type 1, $40 for type 2, and $50 per type 3. There are three operations, each of which limits the amount of production: crushing, grinding, and mixing. In addition, each type of concrete must be inspected. The model has been formulated as: Let X1, X2, and X3 represent respectively the number of type 1, 2, and 3 made in Tonnes per hour.
maximize 30X1 + 40X2 + 50X3
subject to Crushing 2X1 + 4X2 + 5X3 ≤ 80
Grinding 6X1 + 8X2 + 12X3 ≤ 210
Mixing 5X1 + 7X2 + 8X3 ≤ 146
Inspection 3X1 + 4X2 + 5X3 ≥ 50
non-negativity X1 , X2 , X3 ≥ 0
(a) Solve using a spreadsheet Solver, and print the Answer and Sensitivity Reports.
(b) State the solution in words, and indicate which constraints are binding.
(c) By using the information from the Sensitivity Report (NOT by re-running the model each time), give the predicted change to the objective function value (and the reasoning behind your answer) for the following situations (taken one at a time). If the OFV cannot be predicted exactly, then give an answer such as “the OFV will increase by at least $100”.
(i) The revenue per Tonne for type 1 concrete rises by $1.00.
(ii) There are three more units of crushing.
(iii) The revenue per Tonne for type 3 concrete decreases by $8.00.
(iv) The number of units of grinding decreases by 20.
(v) The number of units of mixing increases by 8.
(vi) The price per Tonne of Type 1 cement falls by $3, and the price for Type 3 concrete rises by $15.
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill