Two models of a product - Regular (X) and Deluxe (Y) - are produced by a company. A linear programming model is used to determine the production schedule. The formulation is as follows:

Maximize profit = 50X + 60Y

Subject to:

8X + 10Y=800 (labor hours)

X + Y=120 (total units demanded)

4X + 5Y =500 (raw materials)

all variables =0

The optimal solution is X = 100, Y = 0

How many units of the regular model would be produced based on this solution?

A. 0

B. 50

C. 100

D. 120

In this exercise we have to analyze the functions and mark the alternative that best corresponds, that way we have:

The correct option is C

Here we have maximum profit equal to  

Then we have:

(i) The first equation is:

(ii) The second equation is:

(iii) The third equation is:

From a chart of the above values we have in the most possible region, we have:

Therefore, to maximize profit we have:

Therefore, the number of units of regular model, X for maximum profit should be 100.

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The correct option is;

C. 100

Step-by-step explanation:

Here we have

Maximum profit = 50X + 60Y

8X + 10Y ≤ 800 (labor hours)

X + Y ≤ 120 (total units demanded)

4X + 5Y ≤ 500 (raw materials)

All variables ≥ 0

Then we have

(i) 8X + 10Y ≤ 800

X = 0 or 100

Y = 80 or 0

(ii) X + Y ≤ 120

X = 0 or 120

Y = 120 or 0

(iii) 4X + 5Y ≤ 500

X = 0 or  125

Y = 100 or 0

from a chart of the above values we have in the most possible region, we have

Y intercept at X = 0 and Y = 80

Origin at  X = 0, Y = 0

X intercept at X = 100 and Y = 0

Therefore, to maximize profit we have z(50X + 60Y)

At Y intercept (0, 80) = 4800

At origin = 0

At X intercept (100, 0) = 5000

Therefore, the number of units of regular model, X for maximum profit should be 100.

a

step-by-step explanation:

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let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1