Question 21907: A bakery makes two flavors of cake, chocolate and vanilla and has two ovens, one large and one small. A chocolate-flavored cake requires 10 minutes to bake in the large oven and 40 minutes in the smaller oven. A vanilla-flavored cake requires 20 minutes to bake in the large oven and 30 minutes in the smaller oven. Each day, 600 minutes are available in the large oven and 1200 are available on the small oven. To satisfy the needs of their customers, the bakery must produce at least 6 chocolate-flavored cakes and at least 12 vanilla-flavored cakes. The profit for each chocolate-flavored cake is P50 and the profit for each vanilla-flavored cake is P60.How many of each cake must the bakery make daily to maximize the profit? Draw the detailed graph, indicate the vertices and shade the region enclosed by the constraints.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Let "C" be # of chocolate and "V" number of vanilla.
Inequalities:
10C + 20V <= 600 (this is time in large oven)
Graph C <= -2x+60
40C + 30V <= 1200 (this is time in small over)
Graph C<= (-3/4)V + 30
Graph C>=6 and V>= 12
Graphing these will determine your solution region.
Determine the vertices of this region.
The object function is as follows:
Profit = 50C + 60V
Substitute the individual vertex values
to determine the number of C's and V's
that will give you a maximum profit.
Cheers
stan H.
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