Q1: Al Rabie Housewares Company produces goods A, B and C and the profitof Each of the mentioned products is 150, 100 and 200 dollars, respectively. TheProductionneed into three raw materials M1, M2 and M3. Each unit of theproduced requires 7,4,5 units of M1 and 20,8,10 units of M2 and 20,10,15 unitsof M3 respectively. The raw materials were specified as 1200 units of materialM1, 1500 units of material M2, and 2000 units of material M3.Required: Create a mathematical model that achieves the maximum possibleprofit?

The following steps are used to find the solution of the linear programming problem by the simplex…

Answered: Q1: Al Rabie Housewares Company…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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.
QUESTION 4 Question 7. (A BUSINESS NEEDS WISE PEOPLE) A saleswoman buys the five products say, bag, sunglass, watch, makeup set, and fountain pen from a supplier. Let x = 78, x2 = 25, x3 = 22, x4 = 40 and x5 =10 be the costs respectively. A saleswoman sets a profit of $3 after selling these five products combined. If she sold one item of each product, compute her total sale as: 5 Ex; +3 i=1 QUESTION 5 Question 5.
A trailer manufactor has multiple products designed to be towed by a pickup (Ford F-150, Toyota Tacoma, etc). The production of one of their products - the XL7 5x10 trailer - referred to as XL7510 here, has a fixed 7 cost of $56,048 and a variable cost per unit of XL7510 equal to 214 + - dollars, where is the total number of XL7510s produced. 10 Suppose further that the selling price of this product is 1180 The -values of the break-even points are The maximum revenue is Form the profit function: P(x) = The maximum profit is The price that will maximize profit is 3 10 - dollars per unit of XL7510. dollars (round to the nearest cent) dollars (round to the nearest cent)
f. A drapper is required to supply two types of shirts type A and type B. The total number of shirts must not be more than 400. He has to supply more of type A than type B. However, the number of type A must not be more than 300 and the number of type B shirts must not be less than 80. Let x be the number of type A shirts and y be the number of type B shirts. If the profits were as follows: Type A Ksh 600 per shirt Type B Ksh 400 per shirt. Formulate a Linear Optimization Model, hence use the graphical method to determine the number of shirts of each type that should be made to maximize the profit.
Q1) A retail. Store stocks two types of shirts A and B. These are packed in attractive cardboard boxes. During a week the store can sell a maximum of 400 shirts of type A and a maximum of 300 shirts of type B. The storage capacity, however, is limited to a maximum of 600 of both types combined. Type A shirt fetches a profit of SR 2/- per unit and type B a profit of SR. 5/- per unit. (a) Formulate a mathematical model of the problem.
A building company pays Rp. 100.000, - per day for 50 laden (staff without expertise), Rp. 150,000 to 25 craftsmen 1 (personnel who have expertise in installing ceramics), and Rp. 200.000, - for 25 craftsmen 2 (manpower who have expertise in wood and electricity). What is the average wage paid by the building company for the three types of employees.
Assume that producing 1 unit of calcium requires 0.4 units of calcium, 0.1 units of hydrogen, and 0.1 units of sea salt; that producing 1 nit of hydrogen requires 0.2 units of calcium, 0.3 units of hydrogen, and 0.1 units of sea salt; and that producing 1 unit of sea salt equires 3 units of calcium, 0 units of hydrogen, and 0.2 units of sea salt. Find the production schedule that satisfies an external demand for 41 units of calcium, 39 units of hydrogen, and 11 units of sea salt. X =
XYZ Company has the following capacity per month based on the following: 23 working days per month 1 shift operation at 8 hours per shift. 40 minutes break per shift per employee XYZ company produces bicycles and has the following Capacities per process. Frame Welding: 40 bikes per hour per machine Painting: 20 bikes per hour per worker Assembly : 25 bikes per hour per worker Inspection: 35 bikes per hour per worker If the company needs 3,000 bikes per month, can the company deliver based on the abovementioned capacities? YES or No? Show Excel Computation. No No answer text provided. Yes No answer text provided.
11. Suppose you make and sell skin lotion. A quart of regular skin lotion contains 2 c oil and 1 c cocoa butter. A quart of extra-rich skin lotion contains 1 c oil and 2 c cocoa butter. You will make a profit of $10/qt on regular lotion and a profit of $8/qt on extra-rich lotion. You have 24 c oil and 18 c cocoa butter. a. How many quarts of each type of lotion should you make to maximize your profit? b. What is the maximum profit?
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…

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