sum of the two individual profit components. If, however, the two products compete for
market share in such a way that an increase in sales of one adversely affects the other,
then the additivity property is not satisfied and the model is no longer linear.
3. Certainty: All the objective and constraint coefficients of the LP model are deterministic.
This means that they are known constants-a rare occurrence in real life,
where data are more likely to be represented by probabilistic distributions. In essence,
LP coefficients are average-value approximations of the probabilistic distributions. If
the standard deviations of these distributions are sufficiently small, then the approximation
is acceptable. Large standard deviations can be accounted for directly by using
stochastic LP algorithms (Section 19.2.3) or indirectly by applying sensitivity analysis
to the optimum solution (Section 3.6).
PROBLEM SET 2.1A
1. For the Reddy Mikks model, construct each of the following constraints and express it
with a linear left-hand side and a constant right-hand side:
*(a) The daily demand for interior paint exceeds that of exterior paint by at least 1 ton.
(b) The daily usage of raw material M2 in tons is at most 6 and at least 3.
*(c) The demand for interior paint cannot be less than the demand for exterior paint.
(d) The minimum quantity that should be produced of both the interior and the exterior
paint is 3 tons.
*(e) The proportion of interior paint to the total production of both interior and exterior
paints must not exceed .5.
2. Determine the best feasible solution among the following (feasible and infeasible) solutions
of the Reddy Mikks model:
(a) XI = 1, X2 = 4.
(b) Xl = 2, X2 = 2.
(c) XI = 3, x2 = 1.5.
(d) X I = 2, X2 = 1.
(e) XI = 2, X2 = -l.
*3. For the feasible solution XI = 2, x2 = 2 of the Reddy Mikks model, determine the unused
amounts of raw materials Ml and M2.
4. Suppose that Reddy Mikks sells its exterior paint to a single wholesaler at a quantity discount.
1l1e profit per ton is $5000 if the contractor buys no more than 2 tons daily and $4500
otherwise. Express the objective function mathematically. Is the resulting function linear?
2.2 GRAPHICAL LP SOLUTION
The graphical procedure includes two steps:
1. Determination of the feasible solution space.
2. Determination of the optimum solution from among all the feasible points in the
solution space.
The procedure uses two examples to show how maximization and minimization
objective functions are handled.
ผลรวมของส่วนประกอบแต่ละตัวกำไรสอง ถ้า ไร ผลิตภัณฑ์สองแย่งส่วนแบ่งการตลาดในลักษณะที่เพิ่มขึ้นในการขายของส่งมีผลอื่น ๆแล้วคุณสมบัติ additivity เป็นไม่พอใจ และแบบไม่เชิงเส้น3. ความแน่นอน: ทุกวัตถุประสงค์และข้อจำกัดสัมประสิทธิ์แบบ LP เป็น deterministicหมายความ ว่า พวกเขาเป็นที่รู้จักคงที่หายากเกิดขึ้นในชีวิตจริงซึ่งข้อมูลมีแนวโน้มที่จะแสดง โดยการกระจาย probabilistic ในสาระสำคัญห้างหุ้นส่วนจำกัดสัมประสิทธิ์เป็นเพียงการประมาณค่าเฉลี่ยของการกระจาย probabilistic ถ้าส่วนเบี่ยงเบนมาตรฐานของการกระจายนี้มีขนาดเล็กเพียงพอ แล้วประมาณเป็นที่ยอมรับ ส่วนเบี่ยงเบนมาตรฐานขนาดใหญ่สามารถจะคิดโดยตรงโดยอัลกอริทึม LP สโทแคสติก (ส่วน 19.2.3) หรือโดยทางอ้อม โดยใช้การวิเคราะห์ความไวการแก้ปัญหาเหมาะสม (ส่วน 3.6)ปัญหาชุด 2.1A1. สำหรับรุ่น Mikks เรดดี สร้างข้อจำกัดต่อไปนี้แต่ละ และเอ็กซ์เพรสมันเส้นด้านซ้ายและด้านขวามือคง:*(a) ความต้องการระบายสีภายในประจำวันเกินของสีภายนอก ด้วยน้อย 1 ตัน(b)งานดิบ M2 ในตันเป็น 6 มากที่สุด และน้อย 3*(c) ความต้องการใช้สีภายในไม่น้อยกว่าความต้องการใช้สีภายนอก(d ปริมาณ)ต่ำสุดที่จะผลิตทั้งภายในและภายนอกสีได้ 3 ตัน*(e) The proportion of interior paint to the total production of both interior and exteriorpaints must not exceed .5.2. Determine the best feasible solution among the following (feasible and infeasible) solutionsof the Reddy Mikks model:(a) XI = 1, X2 = 4.(b) Xl = 2, X2 = 2.(c) XI = 3, x2 = 1.5.(d) X I = 2, X2 = 1.(e) XI = 2, X2 = -l.*3. For the feasible solution XI = 2, x2 = 2 of the Reddy Mikks model, determine the unusedamounts of raw materials Ml and M2.4. Suppose that Reddy Mikks sells its exterior paint to a single wholesaler at a quantity discount.1l1e profit per ton is $5000 if the contractor buys no more than 2 tons daily and $4500otherwise. Express the objective function mathematically. Is the resulting function linear?2.2 GRAPHICAL LP SOLUTIONThe graphical procedure includes two steps:1. Determination of the feasible solution space.2. Determination of the optimum solution from among all the feasible points in thesolution space.The procedure uses two examples to show how maximization and minimizationobjective functions are handled.
การแปล กรุณารอสักครู่..
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sum of the two individual profit components. If, however, the two products compete for
market share in such a way that an increase in sales of one adversely affects the other,
then the additivity property is not satisfied and the model is no longer linear.
3. Certainty: All the objective and constraint coefficients of the LP model are deterministic.
This means that they are known constants-a rare occurrence in real life,
where data are more likely to be represented by probabilistic distributions. In essence,
LP coefficients are average-value approximations of the probabilistic distributions. If
the standard deviations of these distributions are sufficiently small, then the approximation
is acceptable. Large standard deviations can be accounted for directly by using
stochastic LP algorithms (Section 19.2.3) or indirectly by applying sensitivity analysis
to the optimum solution (Section 3.6).
PROBLEM SET 2.1A
1. For the Reddy Mikks model, construct each of the following constraints and express it
with a linear left-hand side and a constant right-hand side:
*(a) The daily demand for interior paint exceeds that of exterior paint by at least 1 ton.
(b) The daily usage of raw material M2 in tons is at most 6 and at least 3.
*(c) The demand for interior paint cannot be less than the demand for exterior paint.
(d) The minimum quantity that should be produced of both the interior and the exterior
paint is 3 tons.
*(e) The proportion of interior paint to the total production of both interior and exterior
paints must not exceed .5.
2. Determine the best feasible solution among the following (feasible and infeasible) solutions
of the Reddy Mikks model:
(a) XI = 1, X2 = 4.
(b) Xl = 2, X2 = 2.
(c) XI = 3, x2 = 1.5.
(d) X I = 2, X2 = 1.
(e) XI = 2, X2 = -l.
*3. For the feasible solution XI = 2, x2 = 2 of the Reddy Mikks model, determine the unused
amounts of raw materials Ml and M2.
4. Suppose that Reddy Mikks sells its exterior paint to a single wholesaler at a quantity discount.
1l1e profit per ton is $5000 if the contractor buys no more than 2 tons daily and $4500
otherwise. Express the objective function mathematically. Is the resulting function linear?
2.2 GRAPHICAL LP SOLUTION
The graphical procedure includes two steps:
1. Determination of the feasible solution space.
2. Determination of the optimum solution from among all the feasible points in the
solution space.
The procedure uses two examples to show how maximization and minimization
objective functions are handled.
การแปล กรุณารอสักครู่..
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