Answer:
<h3><u>Part A</u></h3>
Dimensions of tank:
- width = 8.75 in
- length = 8.75 in
- height = 23 in
⇒ Volume of each tank = width × length × height
= 8.75 × 8.75 × 23
= 1760.9375 in³
<h3><u>Part B</u></h3>
Given:
- Hot coffee density = 5.8 oz/in³
- Cold coffee density = 3.5 oz/in³
mass = density × volume
⇒ mass of hot coffee = 5.8 oz/in³ × 1760.9375 in³
= 10213.44 oz (nearest hundredth)
⇒ mass of cold coffee = 3.5 oz/in³ × 1760.9375 in³
= 6163.28 oz (nearest hundredth)
<h3><u>Part C</u></h3>
Convert the masses of the tanks from ounces to pounds
1 lb = 16 oz
⇒ mass of hot coffee tank = 10213.44 ÷ 16
= 638.34 lb (nearest hundredth)
⇒ mass of cold coffee tank = 6163.28 ÷ 16
= 385.21 lb (nearest hundredth)
If the table can hold a maximum of 800 lb:
hot coffee: 800 lb ÷ 638.34 lb = 1.25 (nearest hundredth)
cold coffee: 800 lb ÷ 385.21 lb = 2.08 (nearest hundredth)
Therefore, either:
- 1 tank of hot coffee <u>OR</u>
- 2 tanks of cold coffee
can be placed on a table which can support a maximum weight of 800 lb
Answer:
The combination that gives the most profit is 12 VIP rings and 12 SST rings (900 $/day).
Step-by-step explanation:
This is a linear programming problem.
The objective function is profit R, which has to be maximized.
being V: number of VIP rings produced, and S: number of SST rings produced.
The restrictions are
- Amount of rings (less or equal than 24 a day):
- Amount of man-hours (up to 60 man-hours per day):
- The number of rings of each type is a positive integer:
This restrictions can be graphed and then limit the feasible region. The graph is attached.
We get 3 points, in which 2 of the restrictions are saturated. In one of these three points lies the combination of V and S that maximizes profit.
The points and the values for the profit function in that point are:
Point 1: V=0 and S=24.
Point 2: V=12 and S=12
Point 3: V=20 and S=0
The combination that gives the most profit is 12 VIP rings and 12 SST rings (900 $/day).
Answer:
Slope is 1/2
Y- intercept is -2
Step-by-step explanation:
Re-write the equation so that u have y = x/2 -4/2
Then simplify into y = 1/2x -2
X=4
Explanation
First subtract 4x^2 + 6x from both sides of the equation
X^2 - 8x + 16 = 0
Then let’s factorice the equation using the middle-term break:
x^2 - 4x - 4x + 16 = 0
x (x - 4) - 4 (x - 4) = 0
(x - 4) (x - 4) = 0
(x - 4) ^2 = 0
x = 0
Therefore the solution to the equation is x = 4
If you follow PEMDAS, multiplication would be first, so 3*2 is 6, then it's addition.
So 3*2=6 and 8*-16 is -128, then you add them both.
So 6+(-128) is equals to -122. YOU'RE WELCOME :D