Expert answer:LP questions

Solved by verified expert:I have 3 questions in the attached word doc that I need help with.
questions.docx

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1. The triangle with corners (0,0), (5,10) and (10,5) is convex – like every
triangle. Give constraints that have this triangle as a feasible region. Hint:
You might want to mix  and  .
2. A farmer can plant up to 8 acres of land with wheat and barley. He can earn
$5,000 for every acre he plants with wheat and $3,000 for every acre he
plants with barley. His use of a necessary pesticide is limited by federal
regulations to 10 gallons for his entire 8 acres. Wheat requires 2 gallons of
pesticide for every acre planted and barley requires just 1 gallon per acre.
1. Write down the objective function and if it needs to be minimized or
maximized.
2. Write down all the constraints. [1 pt.O together]
3. Draw the feasible region and explicitly compute all the corner points – don’t
read them off your sketch!
Also evaluate the objective function in these corner points. I’ll give you one
(P1) for free!!!
Mark the optimum solution in the table.
P1
0
0
Objective function
0
P2
____
____
__________
P3
____
____
__________
P4
____
____
__________
3. A hospital needs to assign nurses to six 4 hour shifts. For each shift a certain
minimum number of nurses need to be available
Shift
1
2
3
4
5
6
Time
6am-10am
10am-2pm
2pm-6pm
6pm-10pm
10pm-2am
2am-6am
Minimum # of nurses
70
140
200
85
25
40
A nurse will work two consecutive shifts (so a nurse reporting to shift 6 will also
work shift 1). How many nurses are needed over 24 hours minimally and how
many nurses need to report at the beginning of each shift?
Hint: Let x1, x2, x3, x4, x5, x6 be the number of nurses joining
duty at the beginning of periods 1, 2, 3, 4, 5 and 6, respectively.
1. Write down the objective function and if it needs to be minimized or
maximized.
2. Write down all the constraints. [1 pt together]
3. Solve the problem in R, cut and paste the complete problem definition and
solution into your submission. How many nurses are required over the whole 24
hours? Explicitely write fill in the values in the following table
Shift
1
2
3
4
5
6
Time
6am-10am
10am-2pm
2pm-6pm
6pm-10pm
10pm-2am
2am-6am
Actual # of nurses reporting
______
______
______
______
______
______
…
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