Question

It takes Fena Tailoring 3 hr of cutting and 6 hr of sewing to make a tiered silk organza bridal dress. It takes 6 hr of cutting and 3 hr of sewing to make a lace sheath bridal dress. The shop has at most 30 hr per week available for cutting and at most 24 hr per week for sewing. The profit is $319 on an organza dress and $215 on a lace dress. How many of each kind of bridal dress should be made each week in order to maximize profit? What is the maximum profit? The shop should make organza dresses and lace dresses to yield a maximum profit of $

Answer 1

Let the shop should make x organza dresses and y lace dresses to yield the maximum profit.

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Then according to the given data, we have the following LP problem.

Maximize P = 319x + 215y

Subject to,

3x + 6y ≤ 30

6x + 3y ≤ 24

x ≥ 0, y ≥ 0

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Now let us solve the above LP problem graphically. So we have the following graph.

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-10 5 C (0,5) B (2,4) 15 olo, ) 10 A (4,0)

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So on the above graph, we can notice that the corner points of the feasible region are O(0, 0), A(4, 0), B(2, 4) and C(0, 5)

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Now at O(0, 0), we have, P = (319*0) + (215*0) = 0

Now at A(4, 0), we have, P = (319*4) + (215*0) = 1276

Now at B(2, 4), we have, P = (319*2) + (215*4) = 1498

Now at C(0, 5), we have, P = (319*0) + (215*5) = 1075

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So the shop should make 2 organza dresses and 4​​​​​​ lace dresses to yield a maximum profit of $1498