Question 1067923: Business. Carolyn’s Quality Candy Confectionery is famous for fudge, chocolate crème, and pralines. Its candy-making equipment is set up to make 100-pound batches at a time. Currently there is a chocolate shortage and the company can only get 120 pounds of chocolate in the next shipment. On a weeks run, the confectionery’s cooking and processing equipment is available for a total of 42 machine hours. During the same period, the employees have a total of 56 work hours available for packaging. A batch of fudge requires 20 pounds of chocolate, while a batch of cremes 25 pounds of chocolate. The cooking and processing take 120-minutes for fudge, 150 minutes for chocolate cremes, and 200 minutes for pralines. The packaging times, measuring in minutes per 1 pound box, are 1, 2 and 3, respectively, for fudge, cremes and pralines. Determine how many batches of each type of candy the confectionery should make, assuming that the profit per 1-pound box is 50 cents on fudge, 40 cents on chocolate cremes, and 45 cents on pralines. Also find the maximum profit for the week.
Answer by ikleyn(52788)   (Show Source):
You can put this solution on YOUR website! .
Business. Carolyn’s Quality Candy Confectionery is famous for fudge, chocolate crème, and pralines.
Its candy-making equipment is set up to make 100-pound batches at a time.
Currently there is a chocolate shortage and the company can only get 120 pounds of chocolate in the next shipment.
On a weeks run, the confectionery’s cooking and processing equipment is available for a total of 42 machine hours.
During the same period, the employees have a total of 56 work hours available for packaging.
A batch of fudge requires 20 pounds of chocolate, while a batch of cremes 25 pounds of chocolate.
The cooking and processing take 120-minutes for fudge, 150 minutes for chocolate cremes, and 200 minutes for pralines.
The packaging times, measuring in minutes per 1 pound box, are 1, 2 and 3, respectively, for fudge, cremes and pralines.
Determine how many batches of each type of candy the confectionery should make, assuming that the profit per 1-pound box is
50 cents on fudge, 40 cents on chocolate cremes, and 45 cents on pralines.
Also find the maximum profit for the week.
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Let x, Y and Z be the numbers of batches for fudges, cremes and pralines, respectively.
(Each batch is 100 pounds at a time !)
Then the profit (the objective function) is
P(X,Y,Z) = 50*100X + 40*100Y + 45*100Z cents.
The restrictions are:
20X + 25Y <= 120 (restriction on chocolate amount)
120X + 150Y + 200Z <= 42*60 (restriction on 42 machine hours, written in minutes)
100X + 200Y + 300Z <= 56*60 (restriction on 56 hours packaging time, written in minutes)
The other standard restrictions are X >= 0, Y >= 0, Z >= 0.
Thus the word problem is just reduced to quantitative linear programming problem.
The next step is to input this data into the (appropriate) solver and to press the button "SOLVE".
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