The optimum number of cauliflower and butternut to maximize profit is : 6 Butternuts and 4 Cauliflowers
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<u>Using the Given data : </u>
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
<u>From the table on the amount of Cauliflower the shop owner is prepared to buy and at various unit prices </u>
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
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<em>Since Jacob can only grow and sell 10 vegetables in a week </em>
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 )
Learn more : brainly.com/question/22720939
