Cabinet X costs 60 requires 6 sq f of floor space and holds

Cabinet X costs $60, requires 6 sq f of floor space, and holds 12 cu ft of files. Cabinet Y costs $70, requires 4 sq ft of floor space, and holds 12 cu ft. To get maxium storage, how many of each should be purchased with a budget limit of $630 and floor space of 54 sq ft?

The manager should buy ___ of cabinet X and ___ of Cabinet Y

Solution

Let the number of Cabinet X purchased be a and that of cabinet Y be b. Then 6a + 4b = 54 …(1) and 60a + 70b = 630 or, on dividing both the sides by 10,we have 6a + 7b = 63…(2) On subtracting the 1^st equation from the 2^nd equation, we get 6a + 7b - 6a - 4b = 63 -54 or, 3b = 9 so that b = 3. On substituting b = 3 in the 1^st equation, we get 6a + 4*3 = 54 or, 6a + 12 = 54 or, 6a = 54 -12 = 42 so that a = 42/6 = 7. We can verify the result by substituting a = 7 and b = 3 in the 2^nd equation. On this substitution, we get 6*7 + 7*3 = 63 or, 42 +21 = 63 which is correct. Therefore, the answer is that 7 cabinet X and 3 cabinet Y should be purchased.