Question

A potato processing firm is supplying French fries to a fast food restaurant chain. In the short run under its current facility constraint, each day it can produce the first 1 unit for $2000 variable cost, the second unit for $1500, the third unit for $1900, the fourth unit for $2100, the fifth unit for $2500, and the six unit at $3000 to reach full capacity. The price it sells to the restaurant chain is $2500/unit. The per day (very short run) fixed cost is $1000. (Consider integer for all calculations here.)

If it has a contract to deliver 20 units in a week (no more than five days) how shall it arrange the daily production? [Hint, compare all feasible daily processing levels.] Due to competition, the restaurant chain pushes the price down to $2100/unit.
Now, how shall it adjust the daily production?

What is the profit level a day now?

Realizing the market pressure, the processor decides to invest in new facility for next year (long run). Now, the processor adds a processing line at the cost of $1500 a day, while reducing its marginal cost by $500 for every unit.

What is the new optimal processing level a day?

At this level, what is the new profit?

Answer 1

Computation of contribution per unit
	6 Units	5 Units	4 Units	3 Units	2 Units	1 Unit
First Unit	2000	2000	2000	2000	2000	2000
Second Unit	1500	1500	1500	1500	1500
Third Unit	1900	1900	1900	1900
Fourth Unit	2100	2100	2100
Fifth Unit	2500	2500
Sixth Unit	3000
Total Variable Cost	13000	10000	7500	5400	3500	2000
Variable Cost per unit	2167	2000	1875	1800	1750	2000
Sale Price(per unit)	2500	2500	2500	2500	2500	2500
Contribution per unit	333	500	625	700	750	500
Rank	5	4	3	2	1	4
Option 1
6 Units produced each day for three days and 2 units produced for one day
	3 days	1 day
	18 Units	2 Units	Total
Contribution per unit	$333	$750
Units produced (6*3)	18	2
Contribution (Total)	$5,994	$1,500	$7,494
Option 2
5 Units produced each day for four days
	20 Units
Contribution per unit	$500
Units produced	20
Contribution (Total)	$10,000
Option 3
5 Units produced each day for three days and 3 and 2 units produced on fourth and fifth day
	3 Days	4th Day	5th Day
	15 Units	3 Units	2 units	Total
Contribution per unit	$500	$700	$750
Units produced	15	3	2
Contribution (Total)	$7,500	$2,100	$1,500	$11,100
Option 4
4 Units produced each day for five days
	20 Units
Contribution per unit	$625
Units produced	20
Contribution (Total)	$12,500
Option 5
6 Units produced each day for two days and 4 units produced for one day and 2 units produced for two days
	2 days	1 day	2 days
	12 Units	4 Units	2 Units	Total
Contribution per unit	$333	$625	$750
Units produced	12	4	4
Contribution (Total)	$3,996	$2,500	$6,496	$12,992
Option 5
6 Units produced each day for two days and 3 units produced for two days and 2 units produced for one day
	2 days	2 days	1 day
	12 Units	3 Units	2 Units	Total
Contribution per unit	$333	$700	$750
Units produced	12	6	2
Contribution (Total)	$3,996	$4,200	$8,196	$16,392
It should choose option 5
If selling price goes down to 2100 per unit then per unit profit will go also down by $400($2500-$2100)
Accordingly, the profit would be:
Contribution as per option 5	$16,392
Less: Price Drop($400*20)	$8,000
Less Fixed Cost	$5,000
Total Profit for week	$3,392
Per day profit	$678
If the processor decides to invest in new facility for next year (long run).
Accordingly, the processor adds a processing line at the cost of $1500 a day, while reducing its marginal cost by $500 for every unit.
Old Contribution as per option 5	$16,392
Add: Decrease in Marginal Cost	$10,000
(500*20 units)
New Contribution	$26,392
Less Fixed Cost	$5,000
Less: Additional Fixed Cost	$7,500
Total Profit for week	$13,892
Per day profit	$2,778
Note: Fixed Cost is presumed to be incurred irrespective of production