Data Analysis

Data Analysis
3. A Scottish mining company owns two different mines (A and B) from which it extracts iron ore.
The two mines are located in different areas and produce different qualities of ore. Once
mined, the ore is separated into three grades: high-, medium- and low-grade.

Mine A produces .75 tonnes of high-grade ore, 0.25 tonnes of medium-grade ore and 0.5
tonnes of low-grade ore per hour. Mine 8 produces .25 tonnes of high-grade ore, 0.25 tonnes
of medium-grade ore and 1.5 tonnes of low.grade respectively.
The firm has contracts to supply a minimum of 36 tonnes of high-grade ore, 24 tonnes of
medium.grade ore and 72 tonnes of low-grade are per week.
Mine A costs £50 per hour to operate whilst Mine 8 costs £40 per hour.
This information is summarised in the Table below:
Mine Output
(Tonnes of Ore per hour)
Requirements

(Tonnes per week)
Type of Ore A B

High grade 0.75 0.25 36

Medium grade 0.25 0.25 24

Low grade 0.50 1.50 72

Operating cost (£ per hour) 50 40
a)
Write down expressions for the constraints and cost [12 marks] b)
Use the Excel Solver add-in to determine the number of hours per week that [4 marks] each mine should operate in order to minimise cost
c)
Calculate the quantity of each grade of ore that is surplus to requirement at the [4 marks] cost minimising level of output
d)
Check your answers by solving this linear problem using graphical analyses:
i. Sketch the constraints (you may use computer software if you prefer) [6 marks] ii. Shade in the feasible region and indicate the direction of decreasing cost [6 marks] iii. Determine graphically the cost minimising level of output [6 marks] e)
Confirm your answer algebraically using extreme point theorem [12 marks]

FOR YOUR ASSIGNMENTS TO BE DONE AT A CHEAPER PRICE PLACE THIS ORDER OR A SIMILAR ORDER WITH US NOW