wholesale price p(x) = 90 - 4x, 1 <= x <= 15, with x being quantity sold

[Zyepher]

Business Math - I need full answer xD thanks!

A smartphone manufacturer wholesales the smartphone to retail outlets throughout the South East Asia. It was found that the wholesale price is based on the quantity sold with the function

p(x) = 90 - 4x, 1 ≤ x ≤ 15

Where p(x) is the wholesale price per mobile phone with x millions of mobile phones sold.

Also, it was known that the fixed cost for manufacturing and selling the mobile phone is RM156 mil and to produce every 1 million units of mobile phone, the cost incurred is RM19 millions. (The marginal cost is RM19 mil per 1 million units of mobile phone sold.)

a. Answer the following questions:

i. Find the total cost for 4 million of mobile phone and 6.5 million of mobile phones respectively.
ii. Find the cost function C(x) for manufacturing and selling the mobile phones.
iii. Find the revenue 6.5 million of mobile phones.
iv. Find the revenue function R(x) for the mobile phones.

b. Sketch the functions C(x) and R(x) on a same graph. On the graph, label the following:
i. Find the break-even quantity and break-even revenue for selling the mobile phones.
ii. Find the profit function, P(x).
iii. How many mobile phone should the manufacturer produce?

Hints:
Production cost = Marginal Cost + Fixed Cost
Revenue = Selling Price x Unit Sold
Profit = Revenue - Production Cost
Break-even happens when revenue equals to production cost.

 

[Deleted member 4993]

A smartphone manufacturer wholesales the smartphone to retail outlets throughout the South East Asia. It was found that the wholesale price is based on the quantity sold with the function

p(x) = 90 - 4x, 1 ≤ x ≤ 15

Where p(x) is the wholesale price per mobile phone with x millions of mobile phones sold.

Also, it was known that the fixed cost for manufacturing and selling the mobile phone is RM156 mil and to produce every 1 million units of mobile phone, the cost incurred is RM19 millions. (The marginal cost is RM19 mil per 1 million units of mobile phone sold.)

a. Answer the following questions:

i. Find the total cost for 4 million of mobile phone and 6.5 million of mobile phones respectively.
ii. Find the cost function C(x) for manufacturing and selling the mobile phones.
iii. Find the revenue 6.5 million of mobile phones.
iv. Find the revenue function R(x) for the mobile phones.

b. Sketch the functions C(x) and R(x) on a same graph. On the graph, label the following:
i. Find the break-even quantity and break-even revenue for selling the mobile phones.
ii. Find the profit function, P(x).
iii. How many mobile phone should the manufacturer produce?

Hints:
Production cost = Marginal Cost + Fixed Cost
Revenue = Selling Price x Unit Sold
Profit = Revenue - Production Cost
Break-even happens when revenue equals to production cost.

What are your thoughts?

Please share your work with us ...even if you know it is wrong

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[stapel]

Business Math - I need full answer

Yes, you do need the full answer. So now's the time to get started working on that! What are your thoughts? What have you tried? How far have you gotten? Where are you stuck?

A smartphone manufacturer wholesales the smartphone to retail outlets throughout the South East Asia. It was found that the wholesale price is based on the quantity sold with the function

p(x) = 90 - 4x, 1 ≤ x ≤ 15

Where p(x) is the wholesale price per mobile phone with x millions of mobile phones sold.

Also, it was known that the fixed cost for manufacturing and selling the mobile phone is RM156 mil and to produce every 1 million units of mobile phone, the cost incurred is RM19 millions. (The marginal cost is RM19 mil per 1 million units of mobile phone sold.)

a. Answer the following questions:

i. Find the total cost for 4 million of mobile phone and 6.5 million of mobile phones respectively.

Do the "4 million" part first:

They told you the fixed cost for producing phones ("fixed" meaning that you pay this, regardless of whether you do any actual production at all). What was this value? (Hint: Read the exercise, and copy down the number they told you.)

They told you the variable cost for producing phones, based on the number of millions of phones. How many millions are they asking you about here? (Hint: Re-read the exercise, and copy down the number they told you.) Then what is the variable cost for this number of millions? (Hint: Multiply the number of millions by the per-million number they gave you.)

The "total" cost is the cost that is the total of the fixed and variable costs. What is this total cost? (Hint: Add the fixed- and variable-cost numbers from above. Simplify to get the total-cost number.)

Now do the exact same process with the number "6.5" instead of "4".

ii. Find the cost function C(x) for manufacturing and selling the mobile phones.

For part (a.i.) above, you worked with specific numbers (first the "4", and then the "6.5"). Now you're doing it with "x". Follow the exact same process, noting that you'll end up with an algebraic formula rather than just a number.

iii. Find the revenue 6.5 million of mobile phones.

They gave you a formula for the price (to wholesalers) for a single phone, in terms of millions of phones sold. If a wholesaler buys 2 million units, then his per-phone price is:

. . . . .\(\displaystyle p(2)\, =\, 90\, -\, 4(2)\, =\, 90\, -\, 8\, =\, 82\)

That is, the wholesaler pays 82 Ringgits for each handset. But he's buying 2 million handsets. So what is his total cost? (Hint: Multiply the per-unit price by the total number of units.) What he pays in to you is your "revenue". So what is your revenue?

To answer this part of the exercise, do the exact same computations, but with the given number instead of my example number.

iv. Find the revenue function R(x) for the mobile phones.

Do the exact same computations as in the previous part, but with "x" instead of "6.5".

...and so forth.

If you get stuck, please reply showing all of your thoughts and efforts, so we can see where you're needing assistance. Thank you!