1 answer

Randi devotes 10 hours per week to making belts and handbags for sale

Question:

Randi devotes 10 hours per week to making belts and handbags for sale. One hour is required to make a belt and two hours are required for a handbag. The material for a belt costs $6 and the material for a handbag costs $9. Randi can afford to spend $50 per week for materials. The profit on one belt is $20 and the profit on one handbag is $45. How many belts and how many handbags should Randi sell in order to obtain the largest possible profit?

Answers

Given:

Workload = 10hrs/wk

MakeBelt = 1 belt/hr at $6/belt

MakeBag = 1 bag/2hrs at $9/bag


MaterialsBudget = $50/wk


ProfitForOneBelt = $20

ProfitForOneBag = $45



If Randi makes 1 bag:

$9/bag in 2 hrs ($50-$9) ($41 and 8 hrs remaining)


then, Randi can make

6 belts in 6 hrs at $6/belt ($41-$36) (8hrs-6hrs) ($5 and 2 hrs remaining) 



If Randi makes 2 bags:

$18/bags in 4 hrs ($50-$18) ($32 and 6 hrs remaining)


then, Randi can make

5 belts in 5 hrs at $6/belt ($32-$30) (6hrs-5hrs) ($2 and 1 hr remaining) 



If Randi makes 3 bags:

$27/bags in 6 hrs ($50-$27) ($23 and 4 hrs remaining)


then, Randi can make

3 belts in 3 hrs at $6/belt ($23-$18) (4hrs-3hrs) ($5 and 1 hr remaining) 



If Randi makes 4 bags:

$36/bags in 8 hrs ($50-$36) ($14 and 2 hrs remaining)


then, Randi can make

2 belts in 2 hrs at $6/belt ($14-$12) (2hrs-2hrs) ($2 and 0 hr remaining) --> Choose this



Therefore,

EarningsBag = 4 bags x ($45 - $9) = 4(36) = $144     ----> ANSWER

EarningsBelt = 2 belts x ($20 - $6) = 2(14) = $28    ----> ANSWER


.

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