QUESTION 1- Anderson Co. produces two popular grades of carpeting among its many other products. In the coming production period, Anderson needs to decide how many rolls of each type of carpet should be produced in order to maximize profit. Each roll of Type A carpet uses 40 units of synthetic fiber, requires 32 hours of production time, and needs 18 units of foam backing. Each roll of Type B carpet uses 35 units of synthetic fiber requires 20 hours of production time, and needs 25 units of foam backing.
The profit per type of Type A carpet is $300 and the profit per roll of type B carpet is $210. In the coming production period, Anderson has 4000 units of synthetic fiber available for use. Workers have been scheduled to provide at least 2200 hours of production time (overtime is a possibility). The company has 1800 units of foam backing available for use.
Formulate the linear programming model for this problem.
Let x = the number of rolls of Type A carpet to make
Let y = the number of rolls of Type B carpet to make
Note: In the last field of the constraints, you should include the sign and the RHS value without space between them (for example <=1000).
Question 2- The Mystic Outdoor Shop mixes two types of grass seed into a blend. Each type of grass has been rated (per pound) according its shade tolerance ability to stand up to traffic, and drought resistance, as shown in the table. Type A seed costs $1 and Type B seed costs $2. If the blend needs to score at, least 300 points for shade tolerance, 500 points for traffic resistance, and 680 points for drought resistance, how many pounds of each seed should be in the blend? How much will the blend cost?
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Type A
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Type B
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Shade Tolerance
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2
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2
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Traffic Resistance
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1
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3
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Drought Resistance
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3
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4
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Let A = the pound of Type A seed in the blend
Let B = the pound of Type B seed in the blend.
Note: for the constraints, in the last field you need to include the sign of the constraint and the RHS (for example: <=600).
QUESTION 3-
Solve the following linear program graphically.
Max 8X + 7Y
s.t. 15X + 5Y ≤ 75
10X + 6Y ≤ 60
X+ Y ≤ 8
X, Y ≥ 0
QUESTION 4- Attach your graph for the previous problem. Only one file can be attached.
QUESTION 5- Use this graph to answer the questions.
Which area (I, II, III, IV, or V) forms the feasible region?
Which point (A, B, C, D, or E) is optimal?
This problem is maximization. Constraints with negative slope are pointing towards the origin, and the constraint with positive slope is pointing up.
QUESTION 6- Does the following linear programming problem exhibit infeasibility, unboundedness, or alternate optimal solutions?
Min 1X+ 1Y
s.t. 5X + 3Y ≤ 30
3X + 4Y ≥ 36
Y ≤ 7
X, Y ≥ 0
The problem is "infeasible", "unbounded" or has "multiple solutions".