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Question 22278: Here's the question...A carpentry shop makes dinner tables and coffee tables. Each week the shop must complete at least 9 dinner tables and 13 coffee tables to be shipped to furniture stores. The shop can produce at most 30 dinner tables and coffee tables combined each week. If the shop sells dinner tables for $120 and coffee tables for $150, how many of each item should be produced for a maximum weekly income? What is the maximum weekly income?? HELP FAST PLEASE!! I am so desperate right now...
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! I'll assume you want to graph the solution process.
Set up an axis system with "d" the horizontal axis and "t" the vertical axis.
d is the #of dinner tables produced; t is the number of coffee tables
Draw a vertical line at d=9 and shade in the area to the right (i.e. d>9)
Draw a horizontal line at t=13 and shade above it (i.e. t> 13)
Form the inequality d+t=30 because the shop can produce at most 30 d's and t's.
Solve that inequality for "t" to get t=-d+30
Draw the line t=-d+30 on your axis.
Find the intersection of the line t=-d+30 and d=9. It is (9,21)
Find the intersection of the line t=-d+30 and t=13. It is (17,13)
You have an Income statement that says Income = 120d + 150t
Substitute (9,21) and then (17,13) into this Income equation to find which
gives the greater Income. That is your maximum Income.
Cheers,
Stan H.
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