# Case study chapter 12 (Linear programming)

Owner of a whole sale computer shop plans to sell two type of computers – a desktop and portable model that will cost ₹ 25000 and ₹ 40000 respectively.(Case study linear programming 1 chapter 12 class 12) Owner of a whole sale computer shop plans to sell two type of computers – a desktop

Based on the above information answer the question

(i) If the number of desktop model and portable model in the stock are x and y , to get maximum profit after selling and store of shop have capacity to keep computer not exceed 250 units, then which of the following is correct ?

(a) x + y = 250             (b)  x + y > 250

(c) x + y ≥ 250             (d) x + y ≤ 250

(ii) If owner of shop does not want to invest more than ₹ 70 lakhs on both type of computer then which of the following is correct ?

(a) x + y ≤ 1000            (b) 5x + 8y ≥ 1400

(c) 5x + 8y ≤ 1400        (d) 5x + 8y = 1400

(iii) If the profit on the desktop model is ₹ 4500 and portable model is ₹ 5000, the profit Z is expressed as
(a) Z = 45x + 50y          (b) Z = 4500x+5000y
(c) Z = 5000x+4500y   (d) Z = x + y

(iv) The number of units of each type of computers which the owner of shop have in stock to get maximum profit is
(a) x = 250, y =100        (b) x = 100, y = 250
(c) x = 200, y = 100       (d) x = 200, y = 50

(v)The maximum profit is
(a) ₹ 11,25,000             (b) ₹11,15,000
(b) ₹ 11,80,000            (d) ₹11,50,000

From question total number of both type of computers will not be exceed 250.

x + y ≤ 250

Maximum investment = ₹ 70 lakhs

Total cost of both type of computers = 25000 x + 40000 y

∴ 25000 x + 40000 y ≤ 70,00,000

⇒      25 x + 40 y ≤ 7000

⇒ 5 x + 8 y ≤ 1400

Profit on x desktop models = ₹  4500 x

Profit on y portable models = ₹ 5000 y

Total profit (Z) = ₹ 4500 x + ₹ 5000 y

We have p = 4500 x + 5000 y, which is to be maximise under constraint

x + y ≤ 250

5 x + 8 y ≤ 1400 Owner of a whole sale computer shop plans to sell two type of computers

Also, OABC is  a feasible region which is bounded.

The coordinates of corner points are O(0, 0), A(250, 0), B(200, 50), C(0, 175).

Now we evaluate at each corner point.

Corner point                   Z = 4500 x + 5000 y

O(0, 0)                                       0

A(250, 0)                            11,25,000

B(200, 50)                        11,50,000  ← maximum

C(0, 175)                            8,75,000

For maximum profit

x( no. of desktop)  = 200

y( no of portable) =  50

For x = 200, y = 50

Maximum profit Z is ₹ 11,50,000

Some Other Case study problem

Question: A dealer Ramprakash residing in a rural area open a shop to start his bussiness. He wishes to purchase a number of ceiling fans and table fans. A ceiling fan costs him ₹ 360 and table fan costs ₹ 240.
Based on the above information answer the question(Case study linear programming 2) A dealer Ramprakash residing in a rural area open a shop to start his bussiness.

(i) If Ramprakash purchases x ceiling fans, y table fans. He has space in his store for at most 20 items, then which of the following is correct ?

(a) x + y = 20               (b)  x + y > 20

(c) x + y < 20                (d) x + y ≤ 20

(ii) If Ramprakash has only ₹ 5760 to invest on both types of fan, then which of the following is correct ?

(a) x + y ≤ 5760                        (b) 360 x + 240 y ≤ 5760

(c) 360 x + 240 y ≥ 5760       (d) 3 x + 2y ≤ 48

(iii) If he expects to sell ceiling fan at a profit of ₹ 22 and table fan for a profit of ₹ 18, then the profit is expressed as
(a) Z = 18x + 22y         (b) Z = 22x + 18y
(c) Z = x + y                   (d) Z ≤ 22 x +18 y

(iv) If he sells all the fans that he buys, then the number x, y of both the type fans in stock to get maximum profit is
(a) x = 10, y = 12         (b) x = 12, y = 8
(c) x = 16, y = 0           (d) x = 8, y = 12

(v) The maximum profit after selling all fans
(a) ₹ 360                    (b) ₹ 560
(c) ₹ 1000                  (d) ₹ 392 Mahindra tractors is India’s leading farm equipment manufacturer. It is the largest tractor selling factory Of people having COVID, 90% of the test detects the disease but 10%  goes undetected. Of people free of COVID 