Best Sell Ltd$.$ has decided to launch a new product in addition to its range of products. The following information is available:

$1.$ The new product may be distributed through any combination of the two company warehouses W$1$ and W$2.$

$2.$ The available monthly production capabilities for the new products are:

$1000$ units at plant A

$2000$ units at plant B

$1000$ units at plant C

$3.$ Three major concentration points of customer demand are at locations E$,$ F and G which are estimated to have a monthly demand of:

$900$ units at E

$800$ units at F

$900$ units at G

$4.$ The unit production costs amount to Sh$\mathrm{.}30,$ Sh$\mathrm{.}40,$ Sh$\mathrm{.}10$ at A$,$ B and C respectively.

$5.$ The unit handling costs at the warehouses amount to Sh$\mathrm{.}20$ and Sh$\mathrm{.}30$ at W$1$ and W$2.$

$6.$ The unit transportation costs from plant to warehouse and unit delivery cost from warehouse to customers are as shown below:

$$

Transportation cost schedule.

Warehouses

W$1$ W$2$

Plants

A

B

C Sh$.$

$60$

$50$

$130$ Sh$.$

$60$

$50$

$40$

Delivery costs schedule

Locations

E F G

Warehouses

A

B Sh$.$

$30$

$50$ Sh$.$

$50$

$30$ Sh$.$

$80$

$90$

Required:

Determine the optimum production and distribution schedule to minimize total cost.

$(12$ Marks$)$

$($Total: $20$ Marks$)$