1 A paint company has two factories. Each factory produces three grades of paint: Premium, Professional and Handyman. Daily production of the two factories in litres of paint is shown in the table below. Factory A Factory B Premium 4000 1000 Professional 2000 2000 Constraint 4: Constraint 5: Handyman 1200 3000 The cost of operating Factory A is $10 500 per day. The cost of operating Factory B is $6000 per day. a Write down an equation that gives the total cost in dollars, C, of running Factory A for x days and Factory B fory days. The company has an order for 100 000 litres of Premium quality paint, 120 000 litres of Professional quality paint and 120 000 litres of Handyman quality paint. The company needs to decide the number of days to operate each of the factories to fill this order at the minimum cost. b If x is the number of days that Factory A needs to operate andy is the number of days that Factory B needs to operate, write down in terms ofx and y the five equations that constrain the solution of this problem. Constraint 1: Constraint 2: Constraint 3: c Use these constraints to graph the feasible region for this problem. Clearly label your graph and the coordinates of all intersection points. Shade the feasible region.
1 A paint company has two factories. Each factory produces three grades of paint: Premium, Professional and Handyman. Daily production of the two factories in litres of paint is shown in the table below. Factory A Factory B Premium 4000 1000 Professional 2000 2000 Constraint 4: Constraint 5: Handyman 1200 3000 The cost of operating Factory A is $10 500 per day. The cost of operating Factory B is $6000 per day. a Write down an equation that gives the total cost in dollars, C, of running Factory A for x days and Factory B fory days. The company has an order for 100 000 litres of Premium quality paint, 120 000 litres of Professional quality paint and 120 000 litres of Handyman quality paint. The company needs to decide the number of days to operate each of the factories to fill this order at the minimum cost. b If x is the number of days that Factory A needs to operate andy is the number of days that Factory B needs to operate, write down in terms ofx and y the five equations that constrain the solution of this problem. Constraint 1: Constraint 2: Constraint 3: c Use these constraints to graph the feasible region for this problem. Clearly label your graph and the coordinates of all intersection points. Shade the feasible region.
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
ChapterP: Prerequisites
SectionP.1: Modeling The Real World With Algebra
Problem 23E: Grade Point Average In many universities students are given grade points for each credit unit...
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Transcribed Image Text:1 A paint company has two factories. Each factory produces three grades of paint: Premium,
Professional and Handyman.
Daily production of the two factories in litres of paint is shown in the table below.
Factory A
Factory B
Premium
4000
1000
Professional
2000
2000
Handyman
1200
3000
The cost of operating Factory A is $10 500 per day. The cost of operating Factory B is
$6000 per day.
a Write down an equation that gives the total cost in dollars, C, of running Factory A for
x days and Factory B fory days.
The company has an order for 100 000 litres of Premium quality paint, 120 000 litres of
Professional quality paint and 120 000 litres of Handyman quality paint. The company
needs to decide the number of days to operate each of the factories to fill this order at the
minimum cost.
b If x is the number of days that Factory A needs to operate andy is the number of days
that Factory B needs to operate, write down in terms ofx and y the five equations that
constrain the solution of this problem.
Constraint 1:
Constraint 2:
Constraint 3:
Constraint 4:
Constraint 5:
c Use these constraints to graph the feasible region for this problem. Clearly label your
graph and the coordinates of all intersection points. Shade the feasible region.
d Use the graph to determine the number of days each factory should be operated to
minimise the cost of filling the order. What is this minimum cost?
e Through a combination of installing new machinery and reducing staff, Factory A can
now can be operated for the same cost as Factory B and still produce the same amount
of paint. So both factories can be operated for $6000 per day. How does this affect the
solution?
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