Answer:
$192
Step-by-step explanation:
The cost function is given as:
C(x)=18x+240
The price function is given as:
p(x)= 90 - 3x
The revenue R(x) is the product of the price and the number of products. It is given by:
R(x) = xp(x) = x(90 - 3x) = 90x - 3x²
The profit P(x) is the difference between the revenue and the cost of production. Therefore:
P(x) = R(x) - C(x) = 90x - 3x² - (18x + 240) = 90x - 3x² - 18x - 240
P(x) = -3x² + 72x - 240
The standard equation of a quadratic equation is ax² + bx + c. The function has a maximum value at x = -b/2a
Since P(x) = -3x² + 72x - 240, the maximum profit is at:
x = -72/2(-3) = 12
at x = 12, the profit is:
P(12) = -3(12)² + 72(12) - 240 = -432 + 864 - 240 = $192
Answer:
a. 0.45 customers
b. 0.0145 hours
c. 1.05 customers
Step-by-step explanation:
Missing word "A vending machine dispenses hot chocolate or coffee. service time is 30 seconds per cup and is constant. customers arrive at a mean rate of 72 per hour, and this rate is Poisson-distributed."
λ = 72 customers per hours
μ = 120 customers per hours
a. Lq = λ²/ 2μ(μ-λ)
Lq = 72² / 2(120)(120-72)
Lq = 9/20
Lq = 0.45 customers
b. Ws = Wq + 1/μ = Lq/λ + 1/μ
Ws = 9/20 customers/72 customers + 1/120 customers
Ws = 0.0145 hours
c. Ls = Lq + r
Ls = 9/20 + 72/120
Ls = 1.05 customers
<span> 3( x + 1 ) = - 2 ( x - 1 ) + 6 </span>
<span>1) Clear the parentheses by distributing the 3 and the - 2 </span>
<span>When you have done that, this is what you will get: </span>
<span>3x + 3 = - 2x + 2 + 6 </span>
<span>2) Combine the like terms on the right </span>
<span>You will get this: </span>
<span>3x + 3 = - 2x + 8 </span>
<span>3) Add 2x to both sides to collect all the x terms together on the same side </span>
<span>When you finish doing that, you will have </span>
<span>5x + 3 = 8 </span>
<span>4) Subtract 3 from both sides to isolate the 5x term alone on one side </span>
<span>You will get </span>
<span>5x = 5 </span>
<span>5) Divide both sides by 5 to isolate x </span>
<span>x = 1 <-- answer</span>
Answer:
18.000054
Step-by-step explanation: