Question

Jason has $12.50 to spend on his weekly supply of sweets, crisps and apples. A bag of crisps costs $0.65, a bag of sweets costs $0.85, and one apple costs $0.50. The total number of packet of crisps, sweets and apples consumed in a week must be at least seven, and he eats at least twice as many packets of sweets as crisp. His new healthy diet also means that total number of packets of sweets and crisps must not exceed one-third of the number of apples. If s, c, and a denote the number of packets of sweets, packets of crisps, and apples respectively, which two of the following represent the constraints defining the feasible region?

(1) 3c+3s less than or equal to a

(2) s greater than or equal to 0.5c

(3) 0.65s+0.85c+0.5a greater than or equal to 12.5

(4) a+c+s > 7

(5) s less than or equal to c-a

(6) 17s+10a+13c greater than or equal to 250

(7) c less than or equal to 2s

(8) a+c+s less than or equal to 7

(9) 3c+3s+a less than or equal to 0

(10) 3s-3c+a less than or equal to 0

Answer 1

Solution: Given, Jason has $12.50 to spend Abagof crisps 6st = 0.65 =0 A bag of sweets cost = $0.85 =s One apple Cost = $0.50 -a Total should be at least seven The constraints de fining the feasible regim are: - 0 3c +385a cts at a = 36+39 sa (G) 18+ [04-113c 4 multiplying with 20 $12.50 )*(20) (0.855 +0.650 +0.50 a = 175 +13° +100 s 250 Hence ① and ② are correct. Cfor giren Conditions)