Carol uses this graduated tax schedule to determine how much income tax she owes. If taxable income is over- But not over-
The tax is:
SO
$7,825
$31.850
$7.825
$31,850
$64.250
$64,250
$97,925
10% of the amount over $0
$782.50 plus 15% of the amount over 7,825
$4,386.25 plus 25% of the amount over 31,850
$12.486.25 plus 28% of the amount over
64.250
$21.915.25 plus 33% of the amount over
97.925
$47,300.50 plus 35% of the amount over
174,850
$97.925
$174,850
$174.850
no limit
If Carol's taxable income is $89,786, how much income tax does she owe, to the nearest dollar?
a $25,140
b. $12,654
$19,636
d. $37,626
C.
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Acaterer knows he will need 60, 50, 80, 40 and 50 dinner napkins on five successive evenings. he can purchase new napkins initially at 25 cents each, after which he can have dirty napkins laundered by a fast one-day laundry service (i. e., dirty napkins given at the end of the day will be ready for use the following day) at 15 cents each, or by a slow two-day service at 8 cents each or both. the caterer wants to know how many napkins he should purchase initially and how many dirty napkins should be laundered by fast and slow service on each of the days in order to minimize his total costs. formulate the caterer’s problem as a linear program as follows (you must state any assumptions you make): a. define all variables clearly. how many are there? b. write out the constraints that must be satisfied, briefly explaining each. (do not simplify.) write out the objective function to be minimized. (do not simplify.)

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