Constraint in an lp model restricts A. value of the objective function
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Solution Verified by Toppr Let number of tennis racket be made is X and number of cricket bat be made is Y Since, tennis bat requires 1.5 hours and cricket bat requires 3 hours of machine time. Also, there is maximum 42 hours of machine time available. ∴1.5X+3Y≤42 ⇒X+2Y≤28 ...(1) Since, tennis bat requires 3 hours and cricket bat requires 1 hours of craftmans time. Also, there is maximum 24 hours of craftmans time available. ∴3X+Y≤24 ...(2) Since, count of an object can't be negative. ∴X≥0,Y≥0 ...(3) We have to maximize profit of the factory. Here, profit on tennis racket is 20 Rs and on cricket bat is 10 Rs So, objective function is Z=20X+10Y Plotting all the constraints given by equation (1), (2) and (3), we got the feasible region as shown in the image.
Hence, (i) 4 tennis rackets and 12 cricket bats must be made so that factory will work at full capacity. (ii) Maximum profit of factory will be 200 Rs
A manufacturer makes two types of toys A and B. Three machines are needed for this purpose and the time (in minutes) required for each toy on the machines is given below:
Each machine is available for a maximum of 6 hours per day. If the profit on each toy of type A is Rs.7.50 and that on each toy of type B is Rs.5, show that 15 toys of type A and 30 of type B should be manufactured in a day to get maximum profit. Download 1.15 Mb. Share with your friends:
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