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How can the constraint facing the Shaping Department be written as an inequality? 

 Fill in the blanks. 

The shadow price of a scarce resource indicates the amount by which contribution would ...............  if an organisation were deprived of one unit of the resource. The shadow price only applies while the extra unit of resource can be obtained at its .................  cost. 

 KP makes 2 products, the K and the P.  

                                                                  K                        P  

                                                                  $                         $ 

Selling price                                          160                    98 

Mat C                                                         20                      0 

Mat D                                                         20                    20 

Labour                                                      60                     40 

Fixed costs per unit                                15                     10 

Labour is in short supply and KP have only 21,000 hours available per month. Labour is paid $20 per hour. 

What is the maximum contribution they can earn in the month? 

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19

【论述题】

Calculate the contribution from each type of project. 

Determine the optimal production plan for the four-week period ending 30 June 20X0, assuming that RAB is seeking to maximise the profit earned. You should use a linear programming graph, identify the feasible region and the optimal point and accurately calculate the maximum profit that could be earned using whichever equations you need. 

 Explain the meaning of a shadow price and calculate the shadow price of qualified researcher time. 

What is the shadow price of one hour of machine time in the Mixing Department? 

A

 $3 

B

 $7 

C

 $10.50 

D

$1,193 

In what circumstances does slack arise? 

A

 At the optimal solution, when the resource used equals the resource available 

B

 At the optimal solution, when a minimum quantity of a resource must be used, and more than that quantity is used 

C

 At the optimal solution, when the resource used is less than the resource available 

D

 At the optimal solution, when a minimum quantity of resource is used 

The following draft annual budget has been prepared for the machining room of a production centre. The machining room makes four components which are then transferred to an assembly and fitting department. 


The machining room has a maximum capacity of 24,000 hours per year, but any quantity of any of the components can be purchased from an external supplier if required. It is essential that the budgeted quantities of all four components be delivered to the assembly and fitting department. This means that some of the budgeted requirement for components will have to be purchased externally. 

In order to optimise the financial return, which component should be purchased externally? 

A

 Component W 

B

 Component X 

C

 Component Y 

D

 Component Z 

A company makes two products, X and Y, with the same machines and the same direct labour workforce. The following information is available for the next budget period. 



During the period there will be a maximum of 20,000 machine hours and 48,000 direct labour hours available, and these resources could be limiting factors on output and sales. If linear programming is used to determine the optimum production quantities of Product X and Product Y, which one of the following would be a constraint in the linear programming model? 

A

 0.3x + 0.2y ≤ 48,000 

B

0.5x + 0.2y ≤ 20,000 

C

 0.6x + 0.3y ≤ 20,000 

D

 0.6x + 0.5y ≤ 48,000