A toy company manufactures two types of doll; a basic version doll; a basic version doll A and a deluxe version doll B. Each doll of type B takes twice as long to produce as one of type. A and the company would have time to ,make a maximum of 2, 000 per day if it produces only the basic version. The supply of plastic is sufficient to produce 1500 dolls per day (both A and B combined). The deluxe version requires a fancy dress of which there are only 600 per day available. If the company makes profit Rs. 3 and Rs. 5 per doll respectively o doll A and doll B; how many of each should be produced per day in order to maximize profit?

Options

A. `800,500`
B. `500,600`
C. `450,450`
D. `1000,500`

Answer

D

Explanation

Let x dolls of type A and y dolls of type B be produced per day to maximise the profit.
The ma l hematical form of the given LPP is as follows: Maximise Z = 3x + 5y Subject to constraints ` x+2y le 2000, `
` x +y le 1500`
`y le 600`
and ` x,y ge 0 `
The feasible region is OA_. PORO whose corner points are O (0, 0), A.,(1500, 0), P (1000, 500),Q (800, 600) and R (0, 600). At O(0, 0),Z=0 At A., (1500, 0), Z = 4500 At P(1000, 500), Z = 5500 (Maximum) At 0 (1800, 600), Z = 5400 At R(0, 600), Z = 3000 Hence, the maximum value of Z is 5500 at point P(1000, 500).