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A company produces fragrances $A$, $B,$ and $C$. There is virtually unlimited market demand for these. Fragrance $A$ sells for \$$10$ per gallon, $B$ for $\$56$ per gallon, and $C$ for $\$100$ per gallon. Producing $1$ gallon of $A$ requires $1$ hour of labor; producing $1$ gallon of $B$ requires $2$ hours of labor plus $2$ gallons of $A$; producing $1$ gallon of $C$ requires $3$ hours of labor plus $1$ gallon of $B$. Any $A$ used to produce $B$ cannot be sold (and same for $B$ used in $C$). A total of $40$ labor hours are available. Formulate a linear program to maximize the company’s revenue

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Hint: calculate the total hours of labor to make a gallon of B and C. You can then find which product produces the maximum revenue per hour. Are you only allowed to make whole gallons of these, or can you make fractional amounts. If whole gallons, make as many whole gallons of the most lucrative product as you can, then turn to the next.

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  • $\begingroup$ That isn't formulating a linear programming model... $\endgroup$ – vonbrand Feb 19 '13 at 1:42
  • $\begingroup$ @vonbrand: but I believe it is the input for one. $\endgroup$ – Ross Millikan Feb 19 '13 at 2:50
  • $\begingroup$ Not exactly, OP should write down how much of each input is required, and figure out what the resrictions are (variables can not be negative, have a maximal value; the different combinations use up finite resources; ...) $\endgroup$ – vonbrand Feb 19 '13 at 3:03

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