finance/math

[jo-joe]

A satellite TV channel charges £1.5 million for a 30-second
commercial on a popular television show, but offers a discount of
£10,000Q^{1/2 for Q advertising slots on the show. Assuming a
company has £0.5 million in fixed costs, find the cost function, in
terms of the number Q of advertising slots the company buys, and
the average cost function.}

 

[tkhunny]

What's your plan? Surely you have at least an effort or two.

 

[jo-joe]

ok... well this is what i have written down.... i put it into a linear equation of the form y=a+bx... y being the cost of the commercial, a being the FC and b being the discount dependant on the amount of commercial slots.... so i have 1500000=500000+10000Q[sup:2rl1ht8g]1/2[/sup:2rl1ht8g].... but I'm not even sure if that right or what to do next.... should I solve for Q?... Am I headin in the right direction? or no....? I dont know anything about cost/ avg cos functions... i did some research online but It wasn't very helpful... And I'm also having problems with a few other questions....

 

[Denis]

£10,000Q^1/2

^{What d'heck is that? The square root of 10000Q ? 10000 times the square root of Q?
Something else?}

 

[Denis]

1500000=500000+10000Q[sup:vkxxel8r]1/2[/sup:vkxxel8r]....

Whoops...didn't see this...

Do you realise that's the same as Q^2 = 100 (after simplifying), so Q = 10 ?

 

[jo-joe]

I know that.... but I still dont understand cost function and average cost function... um... I dont think I even answered the question... :?

 

[tkhunny]

Cost function: f(Q)

Average Cost Function: f(Q) / Q

 

[jo-joe]

Thanks... that was actually quite helpful. So... in the case of my question, what would the cost function be...?

 

[tkhunny]

You are going to buy Q slots.

Undiscounted Costs: \(\displaystyle Q(1500000)\)

Discounts: \(\displaystyle 10000Q^{1/2}\)