Answer to Question #155552 in Operations Research for Jessalyn

Question

suppose a local shoemaker makes two types of shoes: sandal and boots. suppose each pair of sandals requires 8 hours of design and sewing work and 4 hours of assembly and finishing. each pair of boots requires 8 hours of for design and sewing and 12 hours of assembly and finishing. furthermore, the total number of hours allocated for design and sewing for wok is 160 and the total available hours for assembly and finishing work is 180 hours. finally, to ensure quality of the shoes, the pairs of shoes produced must be less than or equal to 15. how many pairs of sandals and how many pairs of boots can be made under these conditions? suppose the selling price on each pair of sandals is p1,500 and the selling price for each pair of boots is p2,000. how many each of each type of shoes should the manufacturer make to earn the greatest sales revenue?

Answer 1

Let m is for sandals , n is for boots.

$\begin{cases} 8m+8n \leqslant160,\\ 4m+12n\leqslant180,\\ m\leqslant15,\\ n \leqslant 15; \end{cases}$

$\begin{cases} m+n \leqslant20,\\ m+3n\leqslant45,\\ m\leqslant15,\\ n \leqslant 15. \end{cases}$

$1500m+2000n \to max.$

$\begin{cases} m+n \leqslant20,\\ m+3n\leqslant45;\\ \end{cases}$

$2n\leqslant 25;$

$n=12, ~m =8.$

And maximum is $1500\cdot 8+2000\cdot 12=36000.$