Bell Computer produces expensive special process control computers in Mexico,

China, and the US$.$ It sells its products only in the US and Japan. Bell estimates it can sell up to $1000$ of its

machines each month in the US and up to $400$ per month in Japan.

The time to assemble a machine is $40$ minutes in Mexico, $45$ minutes in China, and $25$ minutes in the US$.$

The Mexican plant has available $250$ hours$/$month of production time. The China plant has $300$

hours$/$month$,$ and the US plant has $200$ hours$/$month$.$

Bell must decide how to spread production among its three plants, as well as deciding where to ship the

finished units for sale. Variations in production costs, transportation costs, and tariffs result in a profit per

computer that depends on the country where it was assembled and the country where it is sold. The table

below gives the profit $($in US dollars$)$ per computer sold in each market based on the country in which that

unit was assembled.

Due to various trade regulations, Bell$$s Mexican production sold in the US cannot be more than $30\%$ of its

combined US unit sales. Japan requires that at least $20\%$ of sales in Japan be machines made in China. Bell

wants to be sure that its Mexican production is no more than $25\%$ of its total worldwide unit sales. They

also require that at least $40\%$ of its US sales are machines made in North America $($made in the US or

Mexico$).$

Formulate a linear programming model to solve this problem.

Profit Per Machine By Assembly Site and Market

Sold In:

US Japan

Mexico $300225$

Made In: China $245280$

US $290180$

a$.$ CAREFULLY list all your decision variables.

b$.$ Formulate an objective function that will maximize profits on Bell$$s worldwide sales.

$[$Guidance$]$

max:

c$.$ Formulate the LP model that maximizes Bell$$s worldwide profits. Be sure you clearly indicate which

managerial requirement each constraint addresses.

$[$Guidance$]$

Available Capacity

US sales limit

Japanese sales limit

Mexican units in US $<30\%$ US sales

Japan sales restriction

Mexican share of worldwide sales

North American units $>40\%$ US sales

Non$-$negativity constraints