Linear programming; formulate and solve graphically

Alpha Chocolate Company manufactures two popular chocolate bars, the Star bar and the Moon bar. Both

chocolate bars go through the mixing department, where the various ingredients are combined, and then

enter the coating department, where the bars are coated with chocolate. The Star bar is coated with both

white and dark chocolate to produce a swirled effect. A material shortage of an ingredient in the Moon bar

limits production to 300 batches per day. Production data are presented in the following table. Both chocolate

bars are produced in batches of 200 bars.

Use of capacity in hours per batch

of product

Available daily capacity in hours

Star

Moon

Mixing

525

1.5

1.5

Coating

500

2.0

1.0

Management believes that the company can sell all of its daily production of both the Star and Moon bars.

Other data follow:

Star

Moon

Selling price per batch

Cost per batch

Monthly fixed costs (allocated evenly between both products)

300

350

225

100

$375000

$375000

Required:

1. Formulate the objective function and all of the constraints in order to maximise contribution margin. Be

sure to define the variables.

2. How many batches of each type of chocolate bar (Star and Moon) should be produced to maximise the

total contribution margin?

3. Calculate the contribution margin at the optimal solution.