Question

A company produces two varieties of pens: alpha and beta. Each alpha pen needs twice as much labour time as the beta pen. If only beta pens are manufactured, then the company can produce 500 pens per day. The market can take only up to 150 alpha pens and 250 beta pens per day from the company. The profits earned by the company on selling an alpha pen and a beta pen are Rs 8 and Rs 5 respectively. What are the respective numbers of alpha and beta pens that the company needs to produce in order to maximize the profit?

Answer 1

have u find the answer?

Answer 2

4. A hyperbola centered at the origin and having foci on the x-axis passes through the point
(-25/3 , 4). The length of the latus rectum is 18/5 units. What is the eccentricity of the hyperbola?

Answer 3

Okay so let the no. of alpha pens be 'x'x and the no. of beta pens be 'y'.
so, according to the market limitations,
x<150 ...{i}
y<250 ...{ii}


And according to the labour-information provided, I can conclude that each alpha pen takes twice the time taken to produce a beta pen.

So, if only beta type pens are made, then I can make 500 at most, and 250 can be manufactured if only alpha ones being made.

so, if I have 'L' amount of labour available.

That means L/500 goes into making a beta pen.
And L/250 into making a alpha pen
So, labour I use for x alpha pens is xL/250 and for y beta pens is yL/500

so, total labour used = (xL/250) + (yL/500) ≤ L
or,
x/250 + y /500 ≤ 1 ...{iii}

And now, for the profit 'P' --> 8 from each alpha pen and 5 from each beta pen.
So, P = 8x+5y ...{iv}

Now I need to maximise 'P'

And for that I use linear programming!

Answer 4

What do you want us to do with that bunch? o.O

Answer 5

can u help?

Answer 6

r u der?

Answer 7

Anyways, wit this one, let's solve this one:
x<150
y<250
x/250 + y /500 ≤ 1