Explanation of Solution
Formulation of a Linear
In the given table, “A” be the pounds of ingredient “A” used, “B” be the pounds of ingredient “B” used, and “C” be the pounds of ingredient “C” used.
Let “xi” be the pounds of chemical “i” used.
The objective is to minimize the cost of production.
Therefore, the objective function is,
Constraint 1 to 3:
Minimum ingredient A, B, C requirements for the drug.
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Chapter 3 Solutions
Introduction to mathematical programming
- Comet Enterprises assembles hand-held vacuum cleaners and desk fans in Memphis, TN. Each vacuum cleaner requires one electric motor, 4 hours of labor, and 20 ounces of stainless steel, and brings $12 profit. Each fan requires one electric motor, 1 hour of labor, and 10 ounces of stainless steel, and brings $4 profit. There are 100 electric motors, 160 hours of labor, and 1100 ounces of stainless steel available for this week's production. (a) Formulate a linear program to determine Comet's production plan for this week to maximize total profit, that is, how many hand-held vacuum cleaners, and how many desk fans should the company produce.arrow_forwardAt the beginning of month 1, Finco has $400 in cash. At the beginning of months 1, 2, 3, and 4, Finco receives certain revenues, after which it pays bills (see Table 2 below). Any money left over may be invested for one month at the interest rate of 0.1% per month; for two months at 0.5% per month; for three months at 1% per month; or for four months at 2% per month. Use linear programming to determine an investment strategy that maximizes cash on hand at the beginning of month 5. Formulate an LP to maximize Finco’s profit. Table 2 Month Revenues ($) Bills ($) 1 400 600 2 800 500 3 300 500 4 300 250arrow_forwardAt the beginning of month 1, Finco has $400 in cash. At the beginning of months 1, 2, 3, and 4, Finco receives certain revenues, after which it pays bills (see Table 2 below). Any money left over may be invested for one month at the interest rate of 0.1% per month; for two months at 0.5% per month; for three months at 1% per month; or for four months at 2% per month. Use linear programming to determine an investment strategy that maximizes cash on hand at the beginning of month 5. Formulate an LP to maximize Finco’s profit.arrow_forward
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- Problem 5. An Electricity board charges the following rates mentioned in the table for the use of electricity. All users are charged Taka 50 as a meter charge for every month. If any user wants to change/replace his meter, he will be charged taka 2000. The monthly bill will be generated based on ● Customer Category ● Consumed Units ● Phase ● For Category 3 and 5 along with other parameters, you need to also consider flat rate, peak time, and off-peak time. Take input from the user, how many units were consumed during flat rate, peak, or off-peak time. ● Meter Charge Write a program to read the name of the user, Customer Category, Phase, number of units consumed and print out the monthly bill. Note that ● Phase, flat rate, peak time and off-peak time will be appeared based on the customer category. ● The monthly bill will be calculated following the number of Days in a montharrow_forwardThe JAV Company manufactures two types of lamps; Special lamp and regular lamp. Each special lamp requires 4 pounds of brass and each regular lamp requires 8 pounds of brass. During each production period, the company's brass supply limited to 640 pounds. Each special lamp requires 6 hours of milling time in the machines and each regular lamp requires 2 hours of milling time in the machine, The company's machine are available only for 360 hours in each production period. Each special lamp requires 5 light bulbs that must be imported from Hongkong. The importation of these bulb is limited to 200 units. The contribution to profit of each special lamp and regular lamp are P400 and P360 respectively. How many units of the special lamp and regular lamp should be produced per production period in order to maximize the profit?arrow_forwardMississippi Agricultural Co. owns a wheat warehouse with a capacity of 20,000 bushels. At the beginning of month 1, they have 6,000 bushels of wheat. Each month, wheat can be bought and sold at the price per 1000 bushels given in the table below. The sequence of events during each month is as follows: i) The initial stock of wheat is counted. ii) Any amount of wheat up to your initial stock can be sold at the current month's selling price. iii) The company can buy (at the current month's buying price) as much wheat as they want, subject to the warehouse size limitation. Do the following: 1- Formulate an LP that can be used to determine how to maximize the profit earned over the next 10 months and. 2- Solve your LP using AMPL solver python. Month 1 2 3 4 5 6 7 8 9 10 Selling Price Purchase Price 3 6 7 1 4 5 5 1 3 2 ∞∞№343 8 8 2 325 10 2 5arrow_forward
- amyo Manufacturing produces four parts that require the use of a lathe and a drillpress. The two machines operate 10 hours a day. The following table provides the time inminutes required by each part:It is desired to balance the two machines by limiting thedifference between their total operation times to at most 30 minutes. The market demand for each part is at least 10 units. Additionally, the number of units of part 1 may not exceed that of part 2. b)Solve the following problems by B&B:Maximize ?=18?1+14?2+8?3+4?4subject to15?1+12?2+7?3+4?4+?5≤37?1,?2,?3,?4,?5=(0,1) Part 6arrow_forwardAn iron rod is graded based on the following criteria: Magnetite content must be greater than 50 Calcium carbonate must be less than 0.7 Other adulterants must be greater than 5600 The grades are as follows: Grade is A if all three conditions are met. Grade is B if conditions (i) and (ii) are met Grade is C if conditions (ii) and (iii) are met Grade is D if conditions (i) and (iii) are met Grade is E if conditions only one condition is met Grade is F if none of the conditions are met. Write a program in which you ask user to enter the values of Magnetite, Calcium Carbonate and other adulterants. The output will be generated as per the conditions mentioned above. (Put the visible screen shots of the output with 2 to 4 different input variations)arrow_forwardThe public utilities commission has decided that the electric company overcharged its customers for two months last year. To make up the difference to the customers, the commission orders the company to decrease each of the next month’s bills by 10%. The city also levies a 3%utility tax, which is to be applied to the bill before it is discounted. Also, the10% discount does not apply to the utility tax. Assume electricity costs $0.16per kilowatt-hour. Write a program to compute the next month’s electricity bill given the number of kilowatt-hours consumed as inputarrow_forward
- Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole