Whenever Josh goes to his favorite restaurant, he wants to buy tiramisu, his favorite dessert. Despite the fact he would enjoy t
1 answer:
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Answer:
$10.67
Explanation:
Data provided in the question:
Initial cost = $3
Initial selling cost = $5
Initial sales = 4000
with $1 increase in price she loses 300 sales per month
Now,
Let the increase in price which maximizes the profit be '$x'
Therefore,
Final selling price = $5 + x
Final sales = 4000 - 300x
Thus,
Revenue = Final selling price × Final sales
= ( 5 + x)( 4000 - 300x)
= 20,000 - 1500x + 4000x - 300x²
= 20,000 + 2500x - 300x²
Total Cost = Initial cost × Final sales
= 3(4000 - 300x )
= 12,000 - 900x
Now,
Profit = Total revenue - Total cost
or
P = [ 20,000 + 2500x - 300x² ] - [ 12,000 - 900x ]
or
P = 8,000 + 3400x - 300x²
for point of maxima
Thus,
0 = 0 + 3400 - 300(2x)
or
0 = 3400 - 600x
or
600x = 3400
or
x =
Hence,
The price will be = $5 + x =
= $10.67
Answer:
Ans. He must use 2,987.76 pounds of alloy X (Cu=69%) and 2,365.24 pounds of alloy Y (26%=Cu)
Explanation:
Hi, let´s call alloy X the alloy that contains 69% of Cu and alloy Y the one containing 26% of Cu. Since he needs to produce 5,353 pounds of alloy, the first equation that we need to use is the following.
Now, we need this 5,353 pounds of the new alloy to be 50% Cu, therefore, we have to use a portion of alloy X and alloy Y. This is as follows.
And we have already established that X+Y is equal to 5,353, therefore this equation should look like this.
And we solve for X this equation, this as follows.
Now, we use this result and substitute this for X in the first equation like this.
and then, we solve for Y
So, he needs to use 2,365.24 pounds of alloy that contains 26% of Cu, this means that the rest (2,987.76 pounds) must come from the alloy that contains 69% of Cu.
We can check this result by finding the overall Cu obtained by this amounts of alloy, that is
That adds up to 2,676.51 pounds of pure Cu, and since the total weight of the new alloy is 5,353, this amount of copper makes up for:
50% of the total weight.
Best of luck.