Question

A sports shop sold 69 cricket bats in a month. This was 3 less than 6 times the number of tennis rackets sold by the shop in the same month.
Which of the following equations can be used to find the number of tennis rackets (t) sold in that month?

a. (6-3) t=69
b. 3-6 t=69
c. 6t+3=69
d. 6t-3=69​

Answer 1

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

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.

Corner points Value of Z=20X+10Y

A (0,14) 140

B (4,12) 200 (maximum)

C (8,0) 160

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