Production Adjustment. Algebraic Modelling

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philH007

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Business produces two products
A and B
production costs($) A = 2 B = 3
Selling Price ($) A =5 B = 6
Invested in first production run = $240
Profit target = $300

Actual Results of first run: A = Sold out. B = 16 Units left over.
Total sales = $444 Net Profit = $204

Adjustments to second Run: Invest $240 again. Produce as many Units as possible but add remaining 16 Units to second run to maintain same ratio of A and B as in the first run. (Here I believe it's 60 /40 unless I got that wrong as well)
Question: Given this adjustment what net profit can we expect 2nd on the second run if all units of A and B sell out completely?

Totally stumped!
I can't seem to resolve even the first run's Total Sales against the Net Profits when accounting for the 16 left over units.
Textbook has no similar examples leading up to this question.
 
philH007 said:
Business produces two products
A and B
production costs($) A = 2 B = 3
Selling Price ($) A =5 B = 6
Invested in first production run = $240
Profit target = $300

Actual Results of first run: A = Sold out. B = 16 Units left over.
Total sales = $444 Net Profit = $204

Adjustments to second Run: Invest $240 again. Produce as many Units as possible but add remaining 16 Units to second run to maintain same ratio of A and B as in the first run. (Here I believe it's 60 /40 unless I got that wrong as well)
Question: Given this adjustment what net profit can we expect 2nd on the second run if all units of A and B sell out completely?

Totally stumped!
I can't seem to resolve even the first run's Total Sales against the Net Profits when accounting for the 16 left over units.
Textbook has no similar examples leading up to this question.
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Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING

Please share your work/thoughts about this assignment.

Start with:

# of product A produced in first run = A1

# of product B produced in first run = B1

Production cost of first run = A1 * 2 + B1 * 3

Revenue from first run = A1 * 5 + (B1 - 16) * 6

I think I see your problem - but share your work (then we will discuss)

continue.......
 
Business produces two products

A and B

production costs($) A = 2, B = 3

Selling Price ($) A =5, B = 6

Investment in first production run = $240

Profit target = $300

Actual Results of first run:

A = Sold out. B = 16 units left over.

Total sales = $444

Net Profit = $204


Investment of $240 in first production run (Owner’s Equity).

Product A

If x = number of units produced how many units are sold?

What does it cost to make each unit?

How much is each unit sold for?

Product B

If y = number of units produced how many units are sold given that there are 16 left over?

What does it cost to make each unit?

How much is each unit sold for?

We know:

sales of A + sales of B = 444

sales(A+B) - cost(A +B) = 204

Can you complete both equations and solve for x and y?

Out of 100 units produced in the first run how many are A and how many B?


Adjustments to second Run:

Invest $240 again. Produce as many units as possible but add remaining 16 units to second run to maintain same ratio of A and B as in the first run.

Maximum possible units produced = 100

If we add 16 B (left over from first run) there is a total of 116 units for the second run which are all sold.

Out of this 116 how many are A and how many are B?

Remember to split the total in the same ratio as the first run.

This means for the second run business will make how many A and how many B before adding in the remaining 16 B to give A:B(first run) = A:B(second run).



Investment of $240 in second production run (Owner’s Equity now $480).

Product A

How many units are made?

How many units are sold?

Cost ?/unit

Sale ?/unit

Product B

How many units are made?

How many units are sold given that there are 16 extra sold from the first run?

Cost ?/unit

Sale ?/unit

Can you write an equation which shows the cost of making the required number of units of A and B?

If 16 extra units of B are sold what is the Sales equation?

What net profit can the owner expect on the second production run?
 
My progress. pardon any formatting errors. Not a math guy and under tight schedule.
Sales Projection: Sales =Profits $300 + Costs $240 = $540 in Sales. (P + C = S)
2x + 3y =240
y=(5-2x)/3
5x + 6 (5-2x/3) = 540
x = 60 , y = 40
Production ratio is 60/40 A to B
Here is where you lose me:
"Invest $240 again. Produce as many units as possible but add remaining 16 units to second run to maintain same ratio of A and B as in the first run. Maximum possible units produced = 100. If we add 16 B (left over from first run) there is a total of 116 units for the second run which are all sold. Out of this 116 how many are A and how many are B? "
I can proceed from this BUT:
How are you allowed to assume 100 is the maximum production leading to 116 units total? If that were the case all I need is 3 x 116 units = 348 (?)
Don't I just need an equation for production that gives me a 60/40 A to B ratio once the extra 16 B units are added post production ($240)?
Here is where I have yet to come up with something that works. Math "Teacher" could/would not answer questions beyond ratio and changed subject. 16 B Prod Cost: 2(16)=48 do I minus this from production cost in equation?
2x + 3y - 48 = 240 (yes this seems wrong to me right away)
y=-2x+288/3
x/(y+16) = 60/40
x =72
y = 32
total Units = 104
total profit = 104(3) = $312 (?)
this seems quite short of the $300 profit from the projection + the profit from the 16 extra B units (48$)
next I try solving for y via the ratio = production equation first
Production
x/(y +16) = 60/40
y= 2x/3 - 16
2x +3y -48 = 240
x = 84
y = 40
profits:
x = 84 , y = 40 +16 (leftover B production)
3(84+56) = $420
check:
Sales - Costs
(84(5)+6(40)+6(16)) - (84(2)+40(3)+16(3))
756-336 = $420
??
 
correction to "Cost: 2(16)=48 do I minus this from production cost in equation? "
change to 3(16) =48 cost of B ( number of extras)
apologies for all other errors.
 
I agree with you Phil that we can’t assume assume 100 units is the maximum number business can produce.
My corrected response below shows 104 units being manufactured on the second run.
Tell me what you think:

Business produces two products A and B.
Production costs($) A = 2, B = 3
Selling Price($) A =5, B = 6
Investment in first production run = $240
Profit target = $300

Actual Results of first run:
A = sold out.
B = 16 units left over.
Total sales = $444
Net profit = $204


Investment of $240 in first production run.
Product A
x = number of units produced.
x units sold.
Cost $2/unit
Sale $5/unit

Product B
y = number of units produced.
(y - 16) units sold.
Cost $3/unit
Sale $6unit

Sales equation:
5x + 6(y-16) = 444
5x + 6y = 540

Profit equation:
Cost = 2x +3y
Sales = 5x + 6(y-16)
204 = 5x + 6(y-16) - (2x+ 3y)
204 = 3x + 3y - 96

3x +3y = 300 (profit target)
x + y = 100
Sub y = 100 - x into 5x + 6y = 540:
5x + 6(100 - x) = 540
600 - x = 540
x = 60
Sub x = 60 into x + y = 100:
60 + y = 100
y = 40

Note that the cost of producing 60 A ($120) and 40 B ($120) is covered by initial investment of $240.

Adjustments to second Run:
Invest $240 again. Produce as many units as possible but add remaining 16 units to second run to maintain same ratio of A and B as in the first run.

Consider possible quantities of A and B that can be produced on second run given that 16 B left over from the first run is added to the B count to give ratio A to B of 3:2 (B = 2/3 of A as in the first run). Remember the cost of production is covered by the second investment of $240.

66A 44B 66A 28B $132 + $84 = $216
69A 46B 69A 30B $138 + $90 = $228
72A 48B 72A 32B $144 + $96 = $240
75A 50B 75A 34B $150 + $102 = $252
78A 52B 78A 36B $156 + $108 = $ 264

Table above shows producing 72 A and 32 B is the best option as this uses up the $240 available to be spent. After adding in the 16 B left over from the first run a total of 72 A and 48 B are sold on the second production run.

Investment of $240 in second production run.
Product A
72 = number of units produced.
72 units sold.
Cost $2/unit
Sale $5/unit

Product B
32 = number of units produced.
48 units sold.
Cost $3/unit
Sale $6unit

Profit equation:
Cost = 2(72)+ 3(32)
= 144 + 96
= 240
Sales = 5(72)+ 6(48)
= 360+ 288
= 648
Profit = 648 - 240
= 408

Owner can expect a net profit of $408 on the second production run.
 
Wow thanks for all that work! I will look it over very carefully as soon as I get a chance to see if I can use it elsewhere to verify.
It was obviously a good question as it raises a lot of issues that anyone could apply to other learning "curves".
 
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