Your supermarket is trying to determine how many meatloaf dinners should be produced on Monday. The Monday demand for meatloaf dinners is normally distributed with a mean of 100 and a standard deviation of 20. The cost of producing a meatloaf dinner is $2.00, and the dinner sells for $7.00. It costs $0.60 at the end of the day to dispose of each unsold dinner. If the only possible production quantities are 100, 110, 120, and 130, what production quantity would you recommend

The recommended production quantity is that which maximizes profit.

Quantity 130

Explanation:

Quantity to produce is the problem here. Remember that this is one of the fundamental questions in the discipline of Economics.

- What to produce?     - For whom to produce?

- How to produce?      - In what quantity?

Possible Production Quantities:

100,  110,  120, and 130

Mean Demand = 100

Standard Deviation = 20

Lowest possible demand = 100 - 20 = 80units

Highest possible demand = 100 + 20 = 120units

* Solve, using the mean demand for each quantity level. Assume also that on every Monday, the minimum possible quantity is what is purchased. That's the safest assumption anyway.

FOR QUANTITY 100,

Revenue = 7×100 = $700      Direct cost = 2×100 = $200

Indirect cost = 0.6×20 = $12          Total cost = 200 + 12 = $212

PROFIT = 700 - 212 = $488

FOR QUANTITY 110,

Revenue = 7×110 = $770        Direct cost = 2×110 = $220

Indirect cost = 0.6×30 = $18           Total cost = 220 + 18 = $238

PROFIT = 770 - 238 = $532

FOR QUANTITY 120,

Revenue = 7×120 = $840        Direct cost = 2×120 = $240

Indirect cost = 0.6×40 = $24           Total cost = $264

PROFIT = 840 - 264 = $576

FOR QUANTITY 130,

Revenue = 7×130 = $910          Direct cost = 2×130 = $260

Indirect cost = 0.6×50 = $30            Total cost = $290

PROFIT = 910 - 290 = $620

Remember, the base assumption is that only the minimum quantity of 80units is bought each Monday. This is the only way to account for wastage; which costs 0.6 dollar per unit. So, the more the quantity produced, the greater the likelihood of wastage.

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