Margaret and Bethany have a lemonade stand for one week each summer.
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Given:
Product A requires 7 board feet of wood and 4 lbs of wicker.
Product B requires 5 board feet of wood and 5 lbs of wicker.
Product C requires 4 board feet of wood and 3 lbs of wicker.
Available wood = 3000 board feet
Available wicker = 1400 lbs
Profit margin of A = $35 per unit
Profit margin of B = $42 per unit
Profit margin of C = $20 per unit
To find:
The linear programming problem for given situation.
Solution:
Let the number of units produced of products A, B and C are x, y and z respectively.
Product A Product B Product C Total
Board feet of wood 7 5 4 3000
wicker 4 5 3 1400
Objective function: Maximize
s.t.,
Board feet of wood :
Wicker :
Number of units cannot be negative. So, .
Therefore, the required LPP is
Maximize
s.t.,
The equation for exponential decay is 
, where <em>a</em> is the initial amount, <em>b</em> = 1 + <em>r</em> (the growth rate as a decimal number) and <em>x</em> is the number of time periods (in this case, minutes). Substituting the information we have:
. To the nearest tenth of a gram, this would be 1.0 grams.