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For (a), total cost each month depends on how many radios (s) are made AND on the cost of the mortgage. Each radio costs $23.55 in materials. So the cost of materials for all the radios each month is $23.55 times "s", the number of radios. The TOTAL cost each month is the cost of all materials PLUS the cost of the mortgage each month. C(s) = 23.55s + mortgage cost = 23.55s + 1077
Part (b) is similar but easier. Total revenue depends only on how many radios, s, are sold. Each radio brings $93.25 in revenue. R(s) = Price per radio sold X number of radios sold R(s) = 93.25 X s R(s) = 93.25s
What about (c)?
Profit = Revenue minus Cost. So, profit from s radios made and sold would be P(s) = R(s) - C(s). Put the responses for parts A and B in to form the function for P(s) and then simplify.
Okay, and how would I do (d) and (e)?
Do you understand graphing lines with x- and y-axis, and finding the x and y intercept? If so, it's the same thing. P(s) would be on the vertical axis (like y) and s would go on the horizontal, like x. Showing all your work would mean substituting in "s = 0" and then solving to get the P(s) intercept, and then substituting in "P(s)=0" and solving to get the s-intercept. The "interpret" part means "what are these intercepts?" The s-intercept is where the line crosses the s-axis, so it's where P(s) = 0, in other words, the number of radios made and sold where PROFIT is zero. The P(s) intercept is what the profit will be when ZERO radios are sold -- and it should be negative because even if he doesn't make any radios, he still has to pay $1077 in mortgage costs each month.
I still don't get it.
which part? Are you ok with the x- and y-axis graphing?
I'm confused where you said to substitute P(s)=0 and solve to get the s intercept.
So, in part c, you have the full function for profit which you get from P(s) = R(s) - C(s). P(s) = 93.25s - (23.55s + 1077) P(s) = 93.25s - 23.55s - 1077 P(s) = 69.70s - 1077 The profit when ZERO radios are sold is P(0) = 69.70(0) - 1077 = -1077, meaning he LOSES $1077 if s=0. But he doesn't actually make a positive profit until he sells enough radios to pay that $1077 mortgage, THEN he actually starts making a profit. So, he might want to know how many radios he has to sell to pay the mortgage. Find that by saying, How many radios does he have to make to just equal the cost of the mortgage, no more, no less. In other words, say P(s) = 0, and find what the "s" is that makes that the case. So: P(s) = 69.70s - 1077 0 = 69.70s - 1077 1077 = 69.70s s = 1077 / 69.70 = about 15.45. This means he needs to make more than 15 radios in order to "break even" and get zero profit (but at least no loss). More than 15 radios means he makes positive profit. 15 radios or less means he is losing money each month.
I forgot to end by saying that the s intercept is that 15.45 number, since that's where P(s) is = 0. Just like the x intercept is the value of x when y is equal 0... it's where the line crosses the x axis, so y is 0. In this case, it's where the profit line crosses the "s axis", and it crosses at P(s) = 0. The ordered pair would be (s, P(s)) = (15.45, 0)
And the ordered pair for the P(s) intercept would be (s, P(s)) = (0, -1077). Plot a line from (0, -1077) to (15.45, 0), and label the vertical axis P(s) and horizontal "s", and you'll see how the intercepts relate to the line and to the work and answers in part (d)
Okay, and what about part (e)?
|dw:1347331616883:dw| Part e is pretty much what I put in last comment -- just plot those 2 points and draw a line through them, except that it doesn't make any sense to have a negative number of radios, so s must be greater than or equal to zero. So make the line start on the vertical P(s) axis at negative 1077 and extend up to the right connecting with (15.45,0) and then continuing on above the s axis