Homework Answers
To maximize the orders, L must be cut into various combinations:
- Length = 4,6,11 = 12300 + 9800 + 5750 = 27850
- Length = 4,8,9 = 12300 + 15250 + 6700 = 34250
Orders from combination 4,8,9 is maximum. Thus it should be used.
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Problem 6: Consider the following cutting stock problem, with input length L = 21. These 21-foot...
Prove that your algorithm works! 6.) Dynamic Consider a modification of the rod-cutting problem in which,...
Prove that your algorithm works!
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Problem 12-1 STAR Co. provides paper to smaller companies whose volumes are not large enough to...
Problem 12-1 STAR Co. provides paper to smaller companies whose volumes are not large enough to warrant dealing directly with the paper mill. STAR receives 100-feet-wide paper rolls from the mill and cuts the rolls into smaller rolls of widths 12, 15, and 30 feet. The demands for these widths vary from week to week. The following cutting patterns have been established: Number of: Pattern 12ft. 15ft. 30ft. Trim Loss 1 0 6 0 10 ft. 2 5 2 0...
Consider the following initial value problem, in which an input of large amplitude and short...
Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function.y′+y=7+δ(t−1),y(0)=0.Find the Laplace transform of the solution. Y(s)=L{y(t)}=Obtain the solution y(t). y(t)=Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t=1. y(t)= { if 0≤t<1, if 1≤t<∞.
(2 points) Consider the following initial value problem, in which an input of large amplitude and...
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Consider the following initial value problem, in which an input of large amplitude and short duration...
Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function: x' +2=1 + (t - 2), X(0) = 0. In the following parts, use h(t – c) for the Heaviside function he(t) if necessary. a. Find the Laplace transform of the solution. L{a(t)}(8) = b. Obtain the solution z(t). (t) c. Express the solution as a piecewise-defined function and think about what happens to the graph of...
(1 point) Consider the following initial value problem, in which an input of large amplitude and...
(1 point) Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function. y" + 167²y = 418(t – 4), y(O) = 0, y'(0) = 0. a. Find the Laplace transform of the solution. Y(s) = L {y(t)} = b. Obtain the solution y(t). yt) = c. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t =...
Consider the following initial value problem, in which an input of large amplitude and short duration...
Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function: x' + x = 9+5(t – 5), x(0) = 0. In the following parts, use h(t – c) for the Heaviside function he(t) if necessary. a. Find the Laplace transform of the solution. L{2(t)}(s) = b. Obtain the solution z(t). (t) = c. Express the solution as a piecewise-defined function and think about what happens to the...
Consider the following initial value problem, in which an input of large amplitude and short duration...
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Consider the following initial value problem, in which an input of large amplitude and short duration...
Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function: x" + 91- x = 318(t – 3), x(0) = 0, x'(0) = 0. In the following parts, use h(t – c) for the Heaviside function he(t) if necessary. a. Find the Laplace transform of the solution. L{x(t)}(s) = b. Obtain the solution z(t). X(t) = c. Express the solution as a piecewise-defined function and think about...
(1 point) Consider the following initial value problem, in which an input of large amplitude and short duration has bee...
(1 point) Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function. "8 6(t 1), y(0) = 3, /(0) = 0. a. Find the Laplace transform of the solution. Y(8)= L{y(t)} = | (3s+e^(-s)-24)/(s^2-8s) b. Obtain the solution y(t) y(t)=1/8(e^(8t-8)-1 )h (t- 1 )+6e^(8t)-3 c. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t 1. if...
Prove that your algorithm works!
6.) Dynamic Consider a modification of the rod-cutting problem in which, in addition to a price p, for each rod, each cut incurs a fixed cost of c. The revenue associated with a solution is now the sum of the prices of the pieces minus the costs of making the cuts. Give a dynamic-programming algorithm to solve this modified problem. Prove that your algorithm works.
(2 points) Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function. yy1+(t-4), y(0)0. a. Find the Laplace transform of the solution. Y(s) = L {y(t)) = b. Obtain the solution y(t) C. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t = 4. if 0st<4, y(t) if 4t< o0.
Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function: x' +2=1 + (t - 2), X(0) = 0. In the following parts, use h(t – c) for the Heaviside function he(t) if necessary. a. Find the Laplace transform of the solution. L{a(t)}(8) = b. Obtain the solution z(t). (t) c. Express the solution as a piecewise-defined function and think about what happens to the graph of...
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