Kyle's Stylin' Tyles makes two models of patio tile, the Connecticut and the Texas. One Connecticut tile uses 17 ounces of clay and needs 68 minutes of Kyle's time. One Texas tile uses 51 ounces of clay and needs only 17 minutes of Kyle's time. He has 255 ounces of clay and can spend 272 minutes making tiles. Kyle can sell each Texas tile for $14 and each Connecticut tile for $49. How many Connecticut tiles should he make to maximize his earnings?
Kyle's Stylin' Tyles makes two models of patio tile, the Connecticut and the Texas. One Connecticut tile uses 17 ounces of clay and needs 68 minutes of Kyle's time. One Texas tile uses 51 ounces of clay and needs only 17 minutes of Kyle's time. He has 255 ounces of clay and can spend 272 minutes making tiles. Kyle can sell each Texas tile for $14 and each Connecticut tile for $49. How many Connecticut tiles should he make to maximize his earnings?
As far as I can see it, the best outcome is to make:
3 Conn. tyles x 17-ounce =51 ounces, - Connecticut tiles
This will take 68 X 3=204 minutes of his time.
That leaves him with:
255 - 51 =204 ounces and,
272 - 204 =68 minutes from which he can make:
204 ounces / 51-ounce tyles =4 Texas tyles and =68/17 =4 tyles for the minutes he has left.
so the final result would be:
3 Conn. tyles X $49 =$147 and
4 Tex. tyles X $14 =$56, for a total of
$147 + $56 =$203 maximum earnings.
OK guys. Take a crack at it!!!!.
+33616 c = number of Connecticut tiles
t = number of Texas tiles
Clay: 17c + 51t = 255
Time: 68c + 17t = 272
Hence:
t = 4. c = 3
Earnings:
E = $(49c + 14t) → $203
+128731 Let x be the number of Connecticut tiles and y be the number of Texas tiles manufactured
We have the following system of constraints
17x + 51y ≤ 255
68x + 17y ≤ 272
And we wish to maximize the objective function
49x + 14y
As shown by the graph, here : https://www.desmos.com/calculator/h5pmmegzom, the corner point of the feasible region that maximizes the profit occurs at (x,y) = (3,4)
So....the maximum profit is 49(3) + 14(4) = $203
