Question

Jacob currently grows and sells 10 butternuts each week to a spaza shop. Each butternut costs R4 to grow and is sold for R7.

Answer 1

The optimum number of cauliflower and butternut to maximize profit is : 6 Butternuts and 4 Cauliflowers

Using the Given data :

cost of producing 1 butternut = R4

selling price of 1 butternut = R7

profit from selling 1 butternut = R7 - R4 = R3

Assume: butternut sold in a week = x ,  Cauliflower sold in a week = y

Unit Cost of producing Cauliflower = R6

From the table on the amount of Cauliflower the shop owner is prepared to buy and at various unit prices

i) when the owner buys 4 Cauliflower

  unit profit = R11 - R6 = R5

ii) When shop owner buys 5 Cauliflower

   unit profit = R10.5 - R6 = R4.5

iii) when shop owner buys 10 Cauliflower

   unit profit = R8 - R6 = R2

Since Jacob can only grow and sell 10 vegetables in a week

The various combination of vegetables that he can grow and sell are as follows.

 x + y = 10       where ; profit on x = R3 , profit on y = R5,  R4.5, R2

i) 0 + 10 = 10     ------------- ( 1 )

  0 + 10(R2) =  R20

ii) 6 + 4 = 10    ---------------- ( 2 )

   6( R3 ) + 4(R5) = R38  ( maximum profit )

iii) 10 + 0 = 10  ------------ ( 3 )

   10(R3) + 0 =  R30

iv) 5 + 5 = 10   -------------- ( 4 )

  5( R3 ) + 5 ( R4.5 ) = R37.5

Hence from the combinations of Cauliflower and butternut the optimum number that would yield the highest profit for Jacob is ; 6 Butternut and 4 Cauliflower )

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