In how many different orders can you line up 8 cards on a table?
2 answers:
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Answer:
1.4650 (the first option in the list of possible answers)
Step-by-step explanation:
Start by isolating the exponential expression on one side of the equal sign, thus subtracting 2 from both sides:
Now, in order to solve for "x", we need to lower the exponent, and for that purpose we use logarithm base "3":
In order to find this logarithm, we use the change of base formula:
which rounded to four decimals gives: 1.4650
The optimal number of pots and plates Josh should make is given from
the graph of the inequalities.
Response:
a. 2·p + a ≤ 50
p ≤ 24
a ≤ 40
b. The coordinates of the vertices of the feasible region are; (24, 2), (40, 5), (0, 40), (24, 0), (0, 0)
c. 40 pots and 5 plates
<h3>How can the optimal number of plates and pots Josh should make be found?</h3>Given:
Number of days Josh has to make pots and plates to sell = 8 days
Weight of each pot = 2 pounds
Weight of each plate = 1 pound
Weight Josh cannot carry = More than 50 pounds
Number plates he can make each da = At most 5 plates
Number of pots he can make each day = At most 5 pots
The profit Josh makes for each plate sold = $12
Profit from each pot sold = $25
a. Let <em>p</em> represent the number of pots Josh makes and let <em>a</em> represent the
number plates. The linear inequalities are;
2·p + a ≤ 50
p ≤ 8 × 3 = 24
p ≤ 24
a ≤ 5 × 8 = 40
a ≤ 40
b. When p = 24, we have;
2 × 24 + a = 50
a = 2
When <em>a</em> = 40, 2·p + 40 = 50, gives;
p = 5
The vertex points are;
The coordinates of the vertices of the feasible region are;
(24, 2), (40, 5), (0, 40), (24, 0), (0, 0)
c. The profit function is; P = 25·p + 12·a
The profit at the vertices are;
To maximize his potential profit, therefore;
- <u>Josh should make 40 pots and 5 plates</u>.
Learn more about linear optimization here: