Sunday. Suppose that the production department wants to meet its daily requirements using onlyfull-time employees. Formulate an LP that the production department can use to minimize thenumber of full time employees who must be hired.DayMondayTuesdayWednesday# of Full-Time Employees Required171315ThursdayFridaySaturdaySunday19141611Incorrect Formulation:X, : the number of employees working on day iMinimize Z- xI + x2 + X3 + X4 + Xs + X6 + X7s.t. XI2 17x2 2 13X) 215X42 19Xs 2 14X6 2 16X)211Xi 20, vi - 1,2..7In this formulation, objective function is not the number of full-time employees. The current objectivefunction counts each employee five times, not once. For example, each employee who starts work onMonday works Monday to Friday and is included in x1, x2. X3, x4 and xs. The key to correctlyformulating this problem is to realize that the production department's primary decision is not howmany people are working each day but rather how many people begin work on each day of the week.Correct Formulation:x: : the number of employees beginning work on day ix,+x, +x,*, + x,217+x, + x, + x,2 13*+x,2 15*X,2 19214Minimize Z- x, +x,**x, +X, + X, +s.t.X, + X, + x, + x, +*, +x, *x, +x, + X,X, +x, +x, + X, +X,X, +x, + x, + X, + x, 211x2 0, V i-2.72 16c) Suppose that the number of workers needed on day i is d.. Let w, be the actual number ofworkers on day i. Formulate an LP where the “cost" of having too many workers on day i is fi(W; – di).d) Suppose that the production department wants to minimize the maximum of the surpluses oneach day (max (w1 – dı, w2 – dz.., w7 –d;)). Formulate an LP.e) Suppose that the production department wants to ensure that at least 30% of the workers haveSunday off. Formulate a constraint for this case.

Name: Sunday. Suppose that the production department wants to meet its dail
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Description: Sunday. Suppose that the production department wants to meet its daily requirements using onlyfull-time employees. Formulate an LP that the production department can use to minimize thenumber of full time employees who must be hired.DayMondayTuesday

Given :Min Z=x1+x2+x3+x4+x5+x6+x7S.t.…

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Sunday. Suppose that the production department wants to meet its daily requirements using o full-time employees. Formulate an LP that the production department can use to minimize number of full time employees who must be hired. Day Monday Tuesday Wednesday Thursday # of Full-Time Employees Required 17 13 15 19 Friday Saturday 14 16 Sunday 11 Incorract Formulation

Sunday. Suppose that the production department wants to meet its daily requirements using o full-time employees. Formulate an LP that the production department can use to minimize number of full time employees who must be hired. Day Monday Tuesday Wednesday Thursday # of Full-Time Employees Required 17 13 15 19 Friday Saturday 14 16 Sunday 11 Incorract Formulation

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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13.
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2. Two products are manufactured in a machining center. The productions times per unit of products 1 and 2 are 10 and 12 minutes, respectively. The total regular machine time is 2500 minutes per day. In anyone day, the manufacturer can produce between 150 and 200 units of product 1, but no more than 45 units of product 2. Overtime may be used to meet the demand at an additional cost of $.50 per minute. Assuming that the unit profits for products 1 and 2 are $6.00 and $7.50, respectively, formulate the problem as an LP model, then solve it using TORA to determine the optimum production level for each product as well as any overtime needed in the center.
Arrange a plan to order from the supplier using Part Period Balancing and Least Unit Cost method. Ordering lead time of the components is 1 period. Then Calculate the total cost of each method.
1. Harimau Paper Sdn. Bhd. converts pulpwood to low, medium and high grade newsprint. The pulpwood requirements for each newsprint, availability of each pulpwood, and selling price (per ton) are shown Table 1. The LP is Pulpwood 1 Pulpwood 2 Pulpwood 3 Price Low grade 2 1 1 RM 900 Max z = 900x₁ + 1000x₂ + 1200x3 2x₁ + 2x₂ + x3 ≤ 180 S.t x₁ + 2x2 + 3x3 ≤ 120 x₁ + x₂ + 2x3 ≤ 160 X1, X2, X3 20 Table 1 Medium grade 2 2 1 RM 1000 High grade 1 3 2 RM 1200 Available (tons) 180 120 160
1- A walnut grower estimates from past records that if 20 trees are planted per acre, theneach tree will average 60 pounds of nuts per year. If, for each additional tree planted peracre, the average yield per tree drops 2 pounds, then how many trees should be planted tomaximize the yield per acre? What is the maximum yield? 2- A multimedia company anticipates that there will be a demand for 20,000 copies of acertain DVD during the next year. It costs the company $0.40 to store a DVD for oneyear. Each time it must make additional DVDs, it costs $250 to set up the equipment.How many DVDs should the company make during each production run to minimize itstotal storage and setup costs? 3- Suppose $5,000 is invested at an annual interest rate of 7%. Compute the balance after10 years if the interest is compounded:a. Annuallyb. Quarterlyc. Monthlyd. Continuously 4- Calculate the second derivative of the function y = f (x) defined by the equationx3 + y3 +3xy + 3y2 + 6x + 6y =0 at the point x…
12. When a certain product is sold at a price of 40 monetary units, 400 items are sold. Each time the price decreases by 0.1 monetary unit, sales increase by 5 units. Denote by x the number of times the price is decreased by 0.1 monetary units. a. Express p and q in terms of x. b. Express x in terms of p. c. Express q in terms of p. Originally, the revenue is 16 000 monetary units. d. Find for which values of p the company has revenue exceeding 16 000 monetary units.
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32. A hardware company sells a lot of low-cost, highvolume products. For one such product, it is equallylikely that annual unit sales will be low or high. Ifsales are low (30,000), the company can sell theproduct for $20 per unit. If sales are high (70,000),a competitor will enter and the company will be ableto sell the product for only $15 per unit. The variablecost per unit has a 20% chance of being $10, a 60%chance of being $11, and a 20% chance of being $12.Annual fixed costs are $20,000.a. Use simulation to estimate the company’s expectedannual profit.b. Find a 95% interval for the company’s annualprofit, that is, an interval such that about 95% ofthe actual profits are inside it.c. Now suppose that annual unit sales, variable cost,and unit price are equal to their respective expectedvalues—that is, there is no uncertainty. Determinethe company’s annual profit for this scenario.d. Can you conclude from the results in parts a and cthat the expected profit from a simulation is…