A logistics company is deciding how to allocate its delivery...

Name: a logistics company is deciding how to allocate its delivery trucks to satisfy its customers during the last week of a special shipping promotion the company can make deliveries to several m 71145
Uploaded: 2023-01-26T05:26:28-08:00
Duration: 8 min 48 s
Channel: Sri K
Description: a logistics company is deciding how to allocate its delivery trucks to satisfy its customers during the last week of a special shipping promotion the company can make deliveries to several m 71145

A logistics company is deciding how to allocate its delivery trucks to satisfy its customers during the last week of a special shipping promotion. The company can make deliveries to several major distribution centers in different cities: Phoenix (P), Washington (W), Fort Lauderdale (F), New York (Y), and Charlotte (C). However, the company only has 80 available driver hours and a $250,000 budget. A delivery trip to Phoenix takes 10 hours and costs $15,000, while earning 1% in customer satisfaction points. A delivery to Washington takes 15 hours, costs $20,000, and earns 1.5%. A trip to Fort Lauderdale takes 16 hours, costs $8,000, and earns 2%. New York requires 2 hours, costs $25,000, and brings in 2%, while a trip to Charlotte takes 18 hours, costs $22,000, and earns 3%. What is the time constraint? Group of answer choices P+1.5W+2F+2Y+3C ≤ 80 P+1.5W+2F+2Y+3C ≤ 250 15P+20W+8F+25Y+22C ≤ 80 10P+15W+16F+2Y+18C ≤ 80

Transcript

00:01 In this question we are having truck type data given in the question so let's simplify first our question with the given data.

00:14 So here is the data table which is provided in the question.

00:19 So this is the truck type.

00:20 We have small, medium and large truck types.

00:23 And these are the cost per truck, 20 ,000, 30 ,000, 50 ,000, so total is 96 ,000.

00:32 Capacity per truck is 2 ,000.

00:35 4 ,500, 7 ,000 and together this is equal to 42 number of trucks and driver needed to per truck is 1, 2 and then 3 so this is the given data and from this data we will consider our data in the spreadsheet model along with the formula so here we can see this is the given data provided over here and number of trucks so the total cost will be calculated with the formula and total capacity is 96 ,000 number of trucks are 28 maximum drivers are 42 and here we can see the formula provided.

01:16 So now as for the question, first part of the question, this is in variables, this is in variables will be objective to minimize the total cost.

01:35 So minimize cost will be as 20 ,000 multiplied by s plus 30 ,000.

01:46 Multiplied by m plus 50 ,000 multiplied by l and now the constraint will be 20 ,000 s plus 4500m plus 7000 l is greater than or equal to 96 ,000 when minimum capacity required per day so here as this will be the minimum capacity required per day so here as this will be the minimum capacity then we can simplify this by s plus m plus l which is equal to 25 and these number of truck drivers or the faculty is available for maximum 25 drugs.

02:44 And again we will do 1 s plus 2m plus 3 l which is less than or equal to 42 which is maximum number of drivers.

02:56 Drivers.

03:01 So here s m and l are less than equal to 0 for non -negativity.

03:09 Negative values will be excluded over here and for solving linear programming as per the given question.

03:17 Here we can see the program should be leveled as we can see in this strange shot of spreadsheet.

03:27 This is our data 96 1842 and here is 96 2542 with the sensitivity considered over here so after this we will get our new values for first we will enter green highlighted cell objective function objective function secondly we will select minimum then third we will we will enter yellow cells, yellow cells, and then fold, we will get our constant on click, then added by click on add, enter the blue cells, blue cells.

04:32 So this dialog box will be appeared as we can see in the stimulation over here.

04:38 I have taken the screenshot again.

04:40 Make the constant variable non -negative selected solving method we will choose here simplex lp so then after this we will get our values like this this will be the output and then after here we can see the result as in written it the sensitivity report so this is the answer for a part now let's move on to the second part to solve our b part of the question in the b part our optimal solution where small is equal to 0, medium is equal to 12 and large is equal to 6...

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