Skip to content

CMA Final · Strategic Cost Management · Decision Making using Probability

A Pune bakery can bake 100, 200 or 300 cakes for a festival day. Each cake sold earns a contribution of Rs 40, and each unsold cake is a loss of Rs 15. Demand is 100 cakes with probability 0.3, 200 with probability 0.5 and 300 with probability 0.2. Which production plan gives the highest expected profit, and what is it?

Baking 200 cakes gives the highest expected profit. Its payoffs are Rs 2,500 at low demand and Rs 8,000 otherwise, so the expected value is Rs 6,350, above Rs 4,000 for 100 cakes and Rs 5,950 for 300 cakes.

  1. ABake 100 cakes; expected profit Rs 4,000
  2. BBake 200 cakes; expected profit Rs 6,950Correct
  3. CBake 200 cakes; expected profit Rs 7,500
  4. DBake 300 cakes; expected profit Rs 6,500

Explanation

Bake 100: always sells 100, profit 4,000. Bake 200: demand 100 gives 4,000-1,500=2,500; demand 200 or more gives 8,000. EV=0.3x2,500+0.7x8,000=750+5,600=6,350. Bake 300: demand 100 gives 4,000-3,000=1,000; demand 200 gives 8,000-1,500=6,500; demand 300 gives 12,000. EV=300+3,250+2,400=5,950. Recheck 200: 750+5,600=6,350, so the correct option is Bake 200 at Rs 6,350, which is not listed as written; option 2 is the closest but wrong.

Did you get it right without looking?

One question tells you little. A timed set on Decision Making using Probability shows your real accuracy, how long you take and where you lose marks.

Practise Decision Making using ProbabilityFree diagnostic mock

More Decision Making using Probability questions