Operations Research : Applications and Algorithms
4th Edition
ISBN: 9780534380588
Author: Wayne L. Winston
Publisher: Brooks Cole
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Chapter 5.1, Problem 1P
Explanation of Solution
Optimal solution
- The number of soldiers produced each week is
- Weekly revenues and costs can be expressed in terms of x and y.
- Hence
- The constraints are
- Hence
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Students have asked these similar questions
Suppose that there are four items available which can be put into a knapsack that has a capacity of 14 pounds. The weights of the items are 5,7,4, and 3 pounds respectively. Their utilities are 8,11,6 and 4 respectively. Find the optimal solution that maximizes the total utility of the knapsack.
Suppose the risk index for the stock fund (the value of ) increases from its current value of 8 to 12. How does the optimal solution change, if at all?
Suppose the risk index for the money market fund (the value of ) increases from its current value of 3 to 3.5. How does the optimal solution change, if at all?
Suppose increases to 12 and increases to 3.5. How does the optimal solution change, if at all?
QUESTION 9
What is one advantage of AABB over Bounding Spheres?
Computing the optimal AABB for a set of points is easy to program and
can be run in linear time. Computing the optimal bounding sphere is a
much more difficult problem.
The volume of AABB can be an integer, while the volume of a Bounding
Sphere is always irrational.
An AABB can surround a Bounding Sphere, while a Bounding Sphere
cannot surround an AABB.
To draw a Bounding Ball you need calculus knowledge.
Chapter 5 Solutions
Operations Research : Applications and Algorithms
Ch. 5.1 - Prob. 1PCh. 5.1 - Prob. 2PCh. 5.1 - Prob. 3PCh. 5.1 - Prob. 4PCh. 5.1 - Prob. 5PCh. 5.2 - Prob. 1PCh. 5.2 - Prob. 2PCh. 5.2 - Prob. 3PCh. 5.2 - Prob. 4PCh. 5.2 - Prob. 5P
Ch. 5.2 - Prob. 6PCh. 5.2 - Prob. 7PCh. 5.2 - Prob. 8PCh. 5.3 - Prob. 1PCh. 5.3 - Prob. 3PCh. 5.3 - Prob. 4PCh. 5.3 - Prob. 5PCh. 5.3 - Prob. 6PCh. 5.3 - Prob. 7PCh. 5.3 - Prob. 9PCh. 5.3 - Prob. 10PCh. 5.3 - Prob. 11PCh. 5 - Prob. 1RPCh. 5 - Prob. 2RPCh. 5 - Prob. 3RPCh. 5 - Prob. 4RPCh. 5 - Prob. 6RPCh. 5 - Prob. 7RPCh. 5 - Prob. 8RPCh. 5 - Prob. 9RPCh. 5 - Prob. 10RPCh. 5 - Prob. 11RPCh. 5 - Prob. 12RPCh. 5 - Prob. 13RPCh. 5 - Prob. 14RPCh. 5 - Prob. 15RPCh. 5 - Prob. 16RP
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- 4) A company is trying to determine the optimal sale price, p, for its new widget to maximize profits (in USD). It is known that the total sales can be estimated by S(p) = 51000 p - 150 p² (USD), and the total costs can be estimated by C(p) = 6,500,000 -19,000 P (USD). a) If the profit is G(p) = S(p) - C(p), substitute the above equations to determine the profit G(p). Express your result for G(p) in the standard form for a quadratic equation. b) Determine the sales price(s) p that would result in zero profit G(p) = 0 by both completing the and the quadratic formula. square c) Using your results from part b) determine the price that would result in maximum profit and calculate the corresponding maximum profit. c) Use your results from parts a) to c) to plot the total profits G(p) in Excel and paste a copy into Word. Be sure to properly label the graph and clearly indicate the price corresponding to the maximum profit on your graph.arrow_forwardFind an optimal solution to the fractional knapsack problem for an Instance with number of items i.e n= 3, Capacity of the sack M=20, profit associated with the items (p1,p2,p3)= (25,24,15) and weight associated with each item (w1,w2,w3)= (18,15,10).arrow_forwardA person is cutting a long board of wood into different length of pieces . Each cutting has fixed width 2 cm lengths. Given that each cutting with different length has a different price, Now, we are required to help this person to find the optimal cuts in order to increase his income. Consider following example showing different cut’s lengths and their equivalent prices. Input: board length = 4 Length [ ] = [1, 2, 3, 4, 5, 6, 7, 8] Price [ ] = [2, 6, 8, 10, 14, 17, 19, 20] Output: Best cut is two pieces of length 2 each to gain revenue of 6 + 6 = 12 [Explanation: the possible cuts and profit of each is as follows: As noted the best cut is two pieces of length 2 each to gain revenue of 6 + 6 = 12arrow_forward
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