Question

File Home Insert Draw Page Layout Formulas Data Review View Help P ower Pivot Share Comments Calibri 0 T A D E 28 0 3 LA 11 C A A A General $ % === E ale Wrap Text Merge & Center er Paste BIU % 9 40.00 Insert Delete Format Ideas | Conditional Format as Cell Formatting Table Styles Styles Sort & Find & Filter Select Editing Clipboard Font Alignment Number Cells Ideas C23 X fic А в G H 05 Some refinery process produce at least two gallons of gasoline for each gallon of fuel oil. Winter heating demands require a volume of at least three million gallons of fuel oil. The demand for gasoline, on the other hand, is not more than 6.4 million gallons a day. o - Nino 09 No: If gasoline is selling for $2.25 per gallon and fuel oil sells for $1.70/gal, how much of each should be produced in order to maximize revenue? Decision Variables: Oblective Function: Constraints:

Answer 1

det the volume of gasoline in gallons = x, - vol of fuel oil and gallows = tz. are produced for I 2 gasoline gallows of gallon - of fuel oil. l x,>= 2x2. other contraints X, L= 6.4 x106 X₂ >= 3x100 revenue : 2.25(x) + 1.70(*) : Decision variables = x,,X₂. objective function' = 2.25*, +1.70x2

а тx49-XI ан , анх £ 415 - - iy: - - - - О>< 't 120 'ят- 71 о *** * * т:< x 10 х, >= 3х10 4 х 19 = 7 "х contraints

I now find the corner points of the shaded region. point A: X₂ = 3x100 *, : 2x, 6x106 1. AC 68100, 3410) point B: x = 6.48106 { x 6.4x10' 3.2x106 X2: }, B: 16.4x10', 3.2X106) point C: x, = 6.4810², X,= 3x106 CoCo.4X109, 3x106)

Now the the value maximum value of x,,X, is of the corner point which gives the largest ratue of 2.25x + 1.70x2. substituting pt A:- 2.25( 6X106) + 1.70(3x106) - $13.6 XIO substituting pt B: - 2.25 ( 64X104)+ 1.70(3.77104) , $. 19.84 X10' $19.58106 substituting pt ca 2.25(6.48100) + 1.70(3x106)

The maximum revenue i 14. 84 хто маж мом х, - b-их р“ quloм 1 л ол y, . 3. 2 хто“ влон