Ben will hire a crane to help the workers put the bundles of shingles on the roo

Question

Ben will hire a crane to help the workers put the bundles of shingles on the roof. There is a limit to the weight the crane can lift at one time, but Ben wants the work done as quickly as possible. Explain to Ben what math he can use so that the crane uses the fewest lifts possible. Ben needs to choose between three brands of shingles to use on the roof. He knows he needs 89 bundles of shingles but each type of shingle weighs a different amount. He needs to take the information he has about the cost of the crane and the amount it can lift to determine the cost of using each brand. The crane costs $350 plus an additional $150 for each hour or part of an hour the crane is used. The crane can make 4 lifts in one hour. Each lift must weigh 650 pounds or less. The weights of a bundle of each brand of shingle can be found in the table below. Complete the table. Show your work. Then decide which brand of shingles Ben should choose. Explain your reasoning.

Explanation / Answer

weight of

each bundle

number of

bundles

in one lift

number

of lifts

number

of hours

total cost

of crane

number of bundles in lift can be less than or equal to 650 /weight of each bundle.

number of lift needed is more than or equal to {89 / (number of bundles in 1 lift)}

number of hours is more than or equal to {number .of lifts /4}

price is 350 + 150* {number of hours}

so for brand A

i)

number of bundles in one lift = 650/75 = 8.66 ,so 8

number of lifts = 89/8 = 11.125 ,so 12

number of hours = 12 /4 = 3

total cost = 350+150*3 = 800

ii) for brand B

number of bundles in one lift = 650/80 = 8.125 ,so 8

number of lifts = 89/8 = 11.125 ,so 12

number of hours = 12 /4 = 3

total cost = 350+150*3 = 800

c) for Brand C

number of bundles in one lift = 650/85 = 7.64 ,so 7

number of lifts = 89/7 = 12.71 ,so 13

number of hours = 13 /4 = 3 ,25 so 4

total cost = 350+150*4 = 950

hence Brand A & Brand B is equally preferable in terms of cost,

but Ben should choose Brand A ,as weight of Brand A is less than others.

shingles

weight of

each bundle

number of

bundles

in one lift

number

of lifts

number

of hours

total cost

of crane

brand A 75 8 12 3 800 brand B 80 8 12 3 800 brand C 85 7 13 4 950

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